Justice LEE, opinion of the Court:

¶ 1 This protracted litigation arises out of a real-property exaction imposed on B.A.M. Development, L.L.C., as a condition of a construction permit for a fifteen-acre residential housing development. The case has been before us twice previously and twice we have remanded for a new trial. This third appeal will be B.A.M.'s last. We bring the case to a close by affirming the trial court in all respects.

I

¶ 2 Salt Lake County's "highway dedication" ordinance applies to developers seeking construction permits for any "parcel of land [abutting a] public street which does not conform to current county [road] width standards." SALT LAKE COUNTY, UTAH, CODE OF ORDINANCES § 15-28-010. Those developers must dedicate and improve the additional street width necessary for conformity with county road-width standards. Id.

¶ 3 B.A.M. Development, L.L.C., applied to Salt Lake County for a development permit in July 1997. B.A.M. proposed to develop a fifteen-acre parcel located at 7700 West 3500 South in unincorporated Salt Lake County. The property abuts State Highway 171, a road owned by the state of Utah and managed by the Utah Department of Transportation (UDOT). As directed by the County's highway-dedication ordinance, B.A.M.'s proposed plat dedicated a 40 ft. wide right of way along Highway 171 — in accordance with then-existing County road-width standards. The County's engineering and development staff approved this application.

¶ 4 The County based its road-width standard for Highway 171 on recommendations from the Wasatch Front Regional Council (WFRC) and UDOT. After the County approved B.A.M.'s application, WFRC and UDOT informed a County engineer that the "currently required" highway width at that location required a dedication of 53 ft., rather than 40 ft. The County updated its road-width standards to reflect this, and the County Planning Commission informed B.A.M. that its development permit would be subject to compliance with the new 53 ft. dedication requirement.

¶ 5 B.A.M. appealed the Planning Commission's decision to the Salt Lake County Board of Commissioners, arguing that the County's grab of an additional 13 ft. amounted to an unconstitutional taking of property. The Board of Commissioners denied B.A.M.'s appeal. B.A.M. then filed suit in the district court, which held a bench trial and ruled in favor of the County. The court of appeals affirmed, but we reversed and remanded for a new trial, holding that the trial court should have applied the rough-proportionality test adopted in Dolan v. City of Tigard, 512 U.S. 374, 114 S.Ct. 2309, 129 L.Ed.2d 304 (1994), to B.A.M.'s takings claim. See B.A.M. Dev., L.L.C. v. Salt Lake Cnty. (B.A.M. I), 2006 UT 2, 128 P.3d 1161. B.A.M. lost again in the second trial, in which the court employed Dolan's rough-proportionality test, and B.A.M. again appealed to this court. Again we reversed, this time on the ground that the trial court had misapplied Dolan's rough-proportionality test. See B.A.M. Dev., L.L.C. v. Salt Lake Cnty. (B.A.M. II), 2008 UT 74, 196 P.3d 601. We instructed the trial court on remand to compare the government's cost of alleviating the development's impact on infrastructure with the cost to B.A.M. of the exaction. Id. ¶¶ 13-14.

¶ 6 After conducting a third trial, the district court made the following findings regarding rough proportionality: (1) the County transportation engineer expects increasing traffic in the area surrounding B.A.M.'s development; (2) the WFRC anticipates alleviating this increased traffic through road-widening projects costing $6,748,700 in 1998 dollar values; (3) these projects "will likely be financed by a combination of government ... funding sources, including federal highway funds and additional State, County, and/or municipal funds"; (4) "the portion of the $6,748,700 total cost that is directly attributable to [B.A.M.'s subdivision] is 5%, or $337,500"; and (5) B.A.M.'s total cost for the additional 13 ft. dedication is $83,997.29. The court concluded that B.A.M.'s cost was significantly less than the government's cost, and that the County's exaction thus did not violate the Dolan rough-proportionality standard.

¶ 7 B.A.M. now appeals the judgment from the third trial, insisting that the trial court's rough-proportionality approach was again erroneous because the court calculated the County's costs too broadly and B.A.M.'s too narrowly. B.A.M. also suggests three additional grounds for reversal.

¶ 8 We review the trial court's legal conclusions de novo and the court's subsidiary factual findings for clear error. Manzanares v. Byington (In re Adoption of Baby B), 2012 UT 8, ¶¶ 40-41, 270 P.3d 486. And as for the mixed question whether the trial court correctly applied the constitutional test, the standard of review is de novo. B.A.M. II, 2008 UT 74, ¶ 5, 196 P.3d 601. We find no error in the trial court's judgment and accordingly affirm.

II

¶ 9 Before addressing the substance of B.A.M.'s appeal, we consider a motion for summary disposition filed in this case by the County. In this motion, the County challenges the timeliness of B.A.M.'s appeal, contending that the appeal fails under the time standards in Utah Rules of Appellate Procedure 4(a) and 4(b). According to the County, B.A.M. did not file within the thirty days prescribed by rule 4(a), and B.A.M.'s posttrial motions were so lacking in substance that they did not qualify for the extension of time allowed by rule 4(b). We disagree and hereby deny the County's motion.

¶ 10 Under rule 4(a), a notice of appeal must be filed "within 30 days after the date of entry of the judgment or order appealed from." The thirty-day filing period is subject to extension under rule 4(b), however, which tolls the filing period upon submission of any of several post-trial motions, including a motion to make additional findings of fact under rule 52(b) of the Utah Rules of Civil Procedure, amend the judgment under rule 59, or grant a new trial under rule 59. UTAH R.APP. P. 4(b)(1), (1)(B), (1)(C), (1)(D). Under rule 4(b)(1), the thirty-day period does not begin to run until the court enters an order ruling on one of those underlying motions.

¶ 11 B.A.M.'s notice of appeal was proper under rule 4(b). After the final judgment entered on July 29, 2010, B.A.M. filed a timely postjudgment motion (on August 6, 2010) entitled, "Motion For New Trial and Motion to Amend Judgment."1 The motion referred expressly to rule 59 and requested a new trial. On its face, then, B.A.M.'s motion seemed to satisfy the tolling requirements of rule 4(b).

¶ 12 Despite B.A.M.'s formal compliance with rule 4(b), the County asks us to disregard the motion's form and to consider its essential character. And because the motion, in the County's view, was in substance a motion to reconsider — in that it was essentially a "rehash" of arguments made during trial — the County contends that rule 4(b)'s tolling provision was not triggered.2

¶ 13 We disagree. B.A.M. filed a motion that — in both form and substance — sought a new trial under rule 59. The motion was captioned as a motion for new trial, it cited rule 59, and it expressly requested a new trial. This is sufficient. Rule 4(b) is triggered by the filing of a motion that is properly styled as one of the motions enumerated in the rule and that plausibly requests the relevant relief.3 B.A.M. easily met those requirements.

¶ 14 As the County notes, B.A.M. did not specify which subsection of rule 59 provided the grounds for its relief. But its memorandum in support of the motion explained in detail the legal errors it believed the court had made, and that suffices under our precedent.4 And although B.A.M.'s arguments were unconvincing and repetitive, neither rule 4(b) nor rule 59 require that a posttrial motion make winning arguments to be procedurally proper.

III

¶ 15 As to the merits, B.A.M. first challenges the legal standards and principles applied by the trial court in ruling in the County's favor on B.A.M.'s claim that the development exaction at issue amounted to an unconstitutional taking of its property. B.A.M.'s arguments build on general principles of property law and constitutional takings principles set forth in Nollan v. California Coastal Commission, 483 U.S. 825, 107 S.Ct. 3141, 97 L.Ed.2d 677 (1987), and Dolan v. City of Tigard, 512 U.S. 374, 114 S.Ct. 2309, 129 L.Ed.2d 304 (1994), and elaborated in our subsequent cases. Those principles are essential to an understanding of the issues before us on appeal, so we begin with a background description of the relevant legal landscape.

¶ 16 A development exaction is a government-mandated contribution of property imposed as a condition of approving a developer's project. Salt Lake Cnty. v. Bd. of Educ., 808 P.2d 1056, 1058 (Utah 1991). One common type of development exaction is a mandatory dedication of land for roads. Id. Such a mandatory dedication implicates the Takings Clause of the U.S. Constitution, which protects private property from governmental taking without just compensation. U.S. CONST. amend. V. Takings law in this field is governed by the U.S. Supreme Court's seminal decisions in Nollan and Dolan.

¶ 17 Under Nollan, the Takings Clause requires a direct relationship — an "essential nexus" — between a condition imposed on a developer and the development's predicted impact on the community. 483 U.S. at 836-37, 107 S.Ct. 3141. Nollan began with the premise that local government may outright deny development permits for any legitimate governmental purpose. Id. at 836, 107 S.Ct. 3141. And it concluded that a dedication exaction is not a taking so long as the exaction "serves the same legitimate police-power purpose as a refusal to issue the permit." Id.

¶ 18 Thus, the relationship between the government's need or purpose for the exaction and the nature of the exaction is critical. Nollan, for example, held that a dedication of land for a beach-front pathway as a condition for receiving a residential building permit did not meet the essential-nexus test because the government's need for beach access was not created by the proposed development. Id. at 838, 107 S.Ct. 3141.

¶ 19 Dolan adds an additional constitutional requirement. It holds that the Takings Clause requires that the extent of a development exaction be "rough[ly] proportional[]" to the "projected impact of [the] proposed development." 512 U.S. at 388, 391, 114 S.Ct. 2309. Thus, under Dolan, a dedication exaction not proportional to projected impacts of a development is a taking. Dolan provides that "[n]o precise mathematical calculation is required," but that local governments "must make some effort to quantify [their] findings" that a dedication will directly offset the impacts of development. Id. at 395-96, 114 S.Ct. 2309.

¶ 20 In B.A.M. II, we interpreted Dolan's rough-proportionality test in the context of the County's requirement that B.A.M. dedicate property for highway use as a condition of a development permit. B.A.M. Dev. L.L.C. v. Salt Lake Cnty. (B.A.M. II), 2008 UT 74, 196 P.3d 601. We instructed the trial court on remand to compare the market value of the exacted property with the cost to the government of alleviating the development's projected increase in traffic volume. Id. ¶ 11. The trial court's task, then, was to measure the dollar value of the 13 ft. strip of land exacted by the County and compare that with the cost of accommodating the highway traffic generated by B.A.M.'s development.

¶ 21 B.A.M. challenges the district court's application of these principles in entering a judgment for the County. First, B.A.M. contends that the trial court should have required the County to produce evidence of direct, out-of-pocket infrastructure costs resulting from the development's impact on traffic, and should have deemed irrelevant costs shared with other government entities. Second, B.A.M. asserts that the trial court incorrectly calculated the cost of the exaction to B.A.M. by limiting the scope of B.A.M.'s claim to a 13 ft. strip of land, rather than the entire 53 ft. strip. We find no reversible error in the trial court's ruling, and affirm.

A

¶ 22 B.A.M. claims that the trial court mishandled the rough-proportionality analysis by considering not just the County's direct costs but also indirect costs such as those imposed on UDOT or covered by federal funding. B.A.M.'s sole argument is that our B.A.M. II decision requires courts to consider costs borne only by the specific government entity that imposes an exaction, not costs to other government entities that share the burden of alleviating the development's impact.

¶ 23 The trial court, of course, did not see things B.A.M.'s way. It found that increased traffic on Highway 171 would require widening existing roads; that these road-widening projects would likely be financed by "a combination of ... federal highway funds and additional State, County, and/or municipal funds"; and that the proportion of cost attributable to B.A.M.'s development was 5% of the entire road-widening, which amounted to $337,500. The court also found that the exaction cost to B.A.M. — $83,997 — was much less than the development's impact on the government. We affirm the trial court and reject B.A.M.'s selective reading of B.A.M. II and narrow view of the rough-proportionality standard.

¶ 24 B.A.M.'s position fails under the express terms of our opinion in B.A.M. II. We held in B.A.M. II that the "Dolan analysis, properly applied, asks whether the imposition on the community of a proposed development is roughly equal to the cost being extracted to offset it." 2008 UT 74, ¶ 14, 196 P.3d 601 (emphasis added). That language was deliberate, and it is dispositive. In embracing a consideration of costs to "the community," we were squarely resolving to encompass costs beyond those borne directly by the County. And that formulation was deliberate, as evidenced by the court's response to a petition for rehearing filed by the County in B.A.M. II on this precise issue. In the petition, the County asked us to clarify that relevant costs encompassed more than those imposed directly on the County, requesting that we remove a footnote that suggested otherwise and asserting that we had "cited no legal authority or precedent in support of" our "narrow measure of costs." And despite B.A.M.'s strident assertions in opposition,5 we removed from the opinion the footnote in question, which would have directed the trial court to consider costs only to the County.6 Thus, the position B.A.M. seeks to vindicate here was squarely rejected in B.A.M. II, and we see no basis for revisiting that decision here.

¶ 25 In any event, B.A.M. cites nothing in support of its costs-to-the-County theory (other than our B.A.M. II decision) and we find no basis for it. B.A.M. points to no cases that have limited the costs in the rough-proportionality analysis to those borne by the specific municipality making the exaction, and Nollan and Dolan seem to cut in favor of including UDOT's costs in the calculus.

¶ 26 The constitutional standards in Nollan and Dolan suggest a connection between the government's purpose for an exaction and the scope of costs a court may consider in conducting the rough-proportionality analysis. In Nollan, the Court held that a development exaction is not a taking if it "serves the same governmental purpose" that denial of a development permit would serve. 483 U.S. at 837, 107 S.Ct. 3141. And Dolan's rough-proportionality requirement is a direct extension of Nollan's governmental-purpose (essential-nexus) test. The Dolan Court held that the extent of an exaction must be related to the extent of governmental need for imposing the exaction. 512 U.S. at 391, 114 S.Ct. 2309. Thus, not only must the nature of an exaction relate to government purpose or need (in that the exaction must alleviate the burdens imposed on infrastructure by the development), but the extent of the exaction must also be roughly proportional to the government's need for infrastructure improvements created by the development.

¶ 27 A proper rough-proportionality analysis must therefore consider the exaction's purpose to define the scope of the relevant governmental costs. And if a local government's purpose encompasses a development's impact not just on the specific government entity imposing the exaction but also costs to the broader community or coordinate government entities, then presumably all such costs count in the rough-proportionality calculus. If so — and B.A.M. has offered no basis for a contrary conclusion — then non-County costs would be relevant in the rough-proportionality analysis to the extent such costs were considered by the County in defining the purpose of its exaction.

¶ 28 The record supports the application of that principle to the facts of this case. The County's purpose for imposing the exaction was to alleviate B.A.M.'s impact (increased traffic) on a state-owned — and state-funded — highway. In fact, the County's roadwidth standard for Highway 171 came directly from WFRC and UDOT. Because the County's purpose for imposing the exaction was to alleviate the development's impact on a state-funded road, the state's costs of improving that road are a proper measure of the development's impact.

¶ 29 Limiting the rough-proportionality analysis to the County's direct costs would fail to connect the Nollan inquiry into government purpose with the Dolan inquiry into government costs. That seems problematic. Nollan and Dolan both require an inquiry into government purpose, which may include alleviating development impacts to the broader governmental community, including increased traffic on state-owned roads.7 And if that government purpose is focused on state-funded roads, one can hardly measure the proportionality between the impact on those roads and the cost of alleviating those impacts without accounting for costs borne by the state.

¶ 30 B.A.M. thus gives us no meaningful reason to reverse the trial court's rough-proportionality review. And on the other hand, the County raises two policy concerns that bolster our reading of Nollan and Dolan. As the County notes, the practical realities of land use and road planning necessitate an interactive, ongoing relationship between the County and UDOT. In unincorporated Salt Lake County, the County is the entity that grants development permits and has the authority to impose exactions. But the state owns Highway 171, UDOT sets its road-width standards (in connection with WFRC), and UDOT manages the funding for its improvements (using a combination of state and federal funds). The County is thus in a unique position to act as an intermediary — a sort of regulatory clearinghouse — between developers and a wide range of other government entities (such as UDOT) that bear the costs imposed by development.

¶ 31 As the County also explains, "major highway expansion projects" typically "involve multiple governmental participants and multiple public funding sources." This common cost-sharing means that a local government entity imposing an exaction will infrequently bear sole financial responsibility for alleviating the impacts of a development. B.A.M.'s view of the rough-proportionality standard would generally eliminate exactions imposed on developments that impact significant, state-owned highways — a result that is both troubling and arguably incompatible with the rationale of the Nollan and Dolan decisions. We accordingly affirm the trial court's inclusion of costs to state, federal, and local government in its rough-proportionality analysis.

B

¶ 32 Next, B.A.M. contends that the trial court improperly narrowed the scope of B.A.M.'s claim by considering only 13 ft. of the exaction, rather than the full 53 ft. strip of land. The trial court concluded that B.A.M.'s claim did not include the entire exaction because the only issue that B.A.M. originally appealed to the County Board of Commissioners was its decision to impose a 53 ft. exaction rather than B.A.M.'s proposed 40 ft. exaction. But B.A.M. insists that this suit is independent from the proceedings before the County Board and thus that the scope of its legal claim should not be limited by the Board's administrative proceedings.

¶ 33 We affirm the trial court without reaching the merits of this argument because the court of appeals conclusively determined this issue in B.A.M. Development, L.L.C. v. Salt Lake County, 2004 UT App 34, ¶¶ 5, 16, 87 P.3d 710. As we stated in B.A.M. I:

B.A.M. Dev., L.L.C. v. Salt Lake Cnty. (B.A.M. I), 2006 UT 2, ¶ 7 n. 2, 128 P.3d 1161.

¶ 34 B.A.M.'s second trial was therefore limited to the 13 ft. "supplemental exaction," as was B.A.M. II's review of that trial, and likewise B.A.M.'s third trial, and thus this appeal. B.A.M. seems to think that our remand for a new trial reopened the door to previously litigated arguments that were conclusively resolved on prior certiorari review. But that notion is foreclosed by our "law of the case" doctrine, "under which a decision made on an issue during one stage of a case is binding in successive stages of the same litigation." Thurston v. Box Elder Cnty., 892 P.2d 1034, 1037 (Utah 1995). Adhering to the law of the case promotes judicial economy and "prevents endless litigation" by parties who have already had a full opportunity to litigate an issue. Suel v. Sec'y of Health & Human Servs., 192 F.3d 981, 984-85 (Fed. Cir.1999). We accordingly reject B.A.M.'s attempt to reopen a matter long since closed in this prolonged litigation.

¶ 35 Thus limited, B.A.M.'s takings claim was properly dismissed by the trial court. The court found that the infrastructure costs attributable to B.A.M.'s development were $337,500, while the cost to B.A.M. of the 13 ft. exaction was $83,997.8 The exaction therefore cost B.A.M. roughly 25% of the impact B.A.M. imposed on the community. Accordingly, the exaction imposed on B.A.M. withstands rough proportionality review regardless of the degree of specificity or equivalency that the rough-proportionality test requires.9

IV

¶ 36 Along with the contention that the trial court incorrectly applied the Nollan-Dolan test, B.A.M. peppers its brief with an array of arguments that are either flatly wrong or inadequately briefed. We reject these arguments on the following grounds.

¶ 37 First, B.A.M. contends that the County's development exaction runs afoul of Banberry Development Corp. v. South Jordan City, 631 P.2d 899 (Utah 1981). According to B.A.M., Banberry created a "7-element test by which the `reasonableness' of an exaction or impact fee might be gauged," and at trial the County failed to produce evidence relating to the Banberry test. Banberry, however, does not apply to dedication exactions. Banberry's factor-based reasonableness analysis applies to subdivision fees, such as water connection fees and park improvement fees. See id. at 902 (limiting its discussion to "the constitutional standards of reasonableness that should govern the validity of subdivision charges").10

¶ 38 Second, B.A.M. claims that the County's exaction is discriminatory because it treats owners of highway-abutting property differently than other property owners. But while B.A.M. refers in passing to the Equal Protection Clause of the Fourteenth Amendment and the uniform operation of laws provision in article I, section 24 of the Utah Constitution, B.A.M. fails to identify any legal standard or provide any reasoned, authority-based analysis of this argument. In light of this inadequate briefing, we decline to address the argument.11

¶ 39 Last, B.A.M. asserts that the trial court improperly refused to receive testimony from B.A.M.'s rebuttal expert witness, J. Craig Smith. But B.A.M. fails to point to any instance in the record where the trial court refused to receive testimony from Smith. On the contrary, the trial court explained to B.A.M.'s attorney that Smith's testimony "should have been part of your case in chief," but that "Smith has assured me that there are things going to the testimony yesterday from [the County's expert witness] that he will be refuting, and I'm happy to hear that, and I'm planning to hear that." B.A.M. also fails to cite any relevant law governing the trial court's admission or exclusion of expert testimony. This inadequately briefed argument does not merit further review.

V

¶ 40 B.A.M. has given us no reason to disturb the trial court's judgment in favor of the County. The court did not err by including in its rough-proportionality analysis costs borne by state government entities; nor did it err by limiting the scope of its review to B.A.M.'s 13 ft. road dedication. And B.A.M.'s remaining arguments are meritless or inadequately briefed. For these reasons, we affirm.

Justice LEE authored the opinion of the Court, in which Chief Justice DURRANT, Associate Chief Justice NEHRING, Justice DURHAM, and Justice PARRISH joined.