opinion of the Court:
1 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.
Io.
12 Salt Lake County's "highway dedication" ordinance applies to developers seeking construction permits for any "parcel of land [abutting al public street which does not conform to current county [road] width standards." Saut Lake County, UrTax, CopE or OrpinancEs § 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 Deрartment 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.
T4 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 Cоunty updated its road-width standards to reflect this, and the County Planning Commission informed BAM. that its development permit would be subject to compliance with the new 58 ft. dedication requirement.
15 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 18 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,
16 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; (8) 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 $837,500"; and (5) B.A.M.'s total cost fоr 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
T7 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. BAM. also suggests three additional grounds for reversal.
1 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),
II
19 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, BAM. did not file within the thirty dаys 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.
110 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 triаl under rule 59. Uran 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.
111 B.A.M.'s notice of appeal was proper under rule 4(b). After the final judgment entered on July 29, 2010, BAM. filed a timely postjudgment motion (on August 6, 2010) entitled, "Motion For New Trial and Motion to Amend Judgment."
112 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 becаuse 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.
113 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
III
T15 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.AM.'s arguments build оn general principles of property law and constitutional takings principles set forth in Nollan v. California Coastal Commission,
116 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.,
{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.
118 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,
[ 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."
120 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 COnty. (B.A.M. II),
{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 seope of B.A.M.'s claim to a 18 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
122 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 BAM. 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.
124 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."
4 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 anаlysis to those borne by the specific municipality making the exaction, and Nollen and Dolan seem to cut in favor of including UDOT's costs in the calculus.
126 The constitutional standards in Nollan and Dolan suggest a connection between the government's purpose for an exaction and the seope of costs a court may consider in conducting the rough-proportionality analysis. In Nolan, 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.
127 A proper rough-proportionality analysis must therefore consider the exaction's purpose to define the seope 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.
1 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 road-width standard for Highway 171 came directly from WFRC and UDOT. Because the County's purpose for imposing the exаction 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.
T80 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 Nolin and Do-lan. As the County notes, the practical realities of land use and road planning nеcessitate 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
131 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.AM.'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
132 Next, B.A.M. contends that the trial court improperly narrowed the seope of B.A.M.'s claim by considering only 18 ft. of the exaction, rather than the full 58 ft. strip of land. The trial court concluded that BAM'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 seope of its legal claim should not be limited by the Board's administrative proceedings.
1383 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,
The court of appeals majority concluded that B.A.M. had preserved for appeal only its objection to the County's claim to the additional thirteen feet of its property. In doing so, it affirmed the trial court's conclusion that B.A.M. had never objected to the initial forty-foot exaction in its administrative appeals before the planning and zoning commission or the Board. Judge Orme dissented from this view, believing that in light of the undeveloped state of the record the court of appeals should interpret more generously B.A.M.'s contentions that it had properly challenged the entire seope of the County's proposed property exaction. We did not grant certiorari on this question, however, and therefore limit our review to the thirteen-foot supplemental exaction.
B.A.M. Dev., L.L.C. v. Salt Lake Cnty. (B.A.M. I),
134 B.A.M.'s second trial was therefore limited to the 18 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.,
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
IV
136 Along with the contention that the trial court incorrectly applied the Nollaon-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.
137 First, B.A.M. contends that the County's development exaction runs afoul of Banberry Development Corp. v. South Jordan City,
138 Second, B.A.M. claims that the County's exaction is discriminаtory 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.
139 Last, BAM. 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
V
T140 BAM. has given us no reason to disturb the trial court's judgment in favor оf 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 BAM's 18 ft. road dedication. And B.A.M.'s remaining arguments are meritless or inadequately briefed. For these reasons, we affirm.
Notes
. B.A.M. also filed a second motion, entitled "Motion to Make and Enter Additional Findings of Fact." Because the motion for new trial was sufficient to trigger rule 4(b), we need not decide whether B.A.M.'s motion to enter additionаl findings of fact would likewise trigger rule 4(b).
. See Gillett v. Price,
. See id. 18 (declining to treat a motion to reconsider as a motion that triggers tolling under rule 4(b) and explaining that "the form of a motion does matter because it directs the court and litigants to the specific ... relief sought"); Workers Comp. Fund v. Argonaut Ins. Co.,
. See Judson v. Wheeler RV Las Vegas, L.L.C.,
. In its rehearing brief, B.A.M. argued brazenly that "[this Court does not need 'authority' for its statements; the Court itself is its own 'authority' and does not, need to be lectured by a party-litigant which has so openly disregarded even the most basic of the constitutional principles herein applicable."
. Compare B.A.M. Dev., L.L.C. v. Salt Lake Cnty.,
It is unclear from the record whether the maintenance of [Highway 171] is the responsibility of the County or of [UDOT]. If widening the road is UDOT's responsibility, then the County arguably would bear no cost resulting from the development's impact, and therefore any exaction relating to the traffic increase would exceed the Dolan standard. If the impact does not affect the County, then it has no right to requirе the developer to contribute.
. B.A.M. does not argue that the County's incorporation of UDOT's guidelines into the County's road-width standards constituted an illegitimate government purpose.
. B.A.M. might have plausibly argued that the cost of the initial 40 ft. exaction is a necessary component of the proportionality calculation regardless of whether the only claim preserved is a challenge to the additional 13 ft. But B.A.M. makes no such argument. It clings instead to its
. See, eg., Ehrlich v. City of Culver City,
. While focusing on Banberry, B.A.M. ignored Call v. City of West Jordan,
. See Uta R.Arp. P. 24(a)(9) ("[Briefs] shall contain ... citations to the authorities, statutes, and parts of the record relied on."); State v. Gomez,