Question

Budget. The Richmond rowing club is planning to enter the Head of the Charles race in Boston and is trying to figure out how much money to raise. The entry fee is $\$ 250$ per boat for the first 10 boats and $\$ 175$ for each additional boat. Find the cost function $C(x)$ as a function of the number of boats the club enters $x$. Find the inverse function that will yield how many boats the club can enter as a function of how much money it will raise.

Name: Problem 67, Chapter 3: Algebra and Trigonometry
Uploaded: 2022-03-27T22:55:13-08:00
Duration: 3 min 12 s
Channel: Suzanne W.

   Budget. The Richmond rowing club is planning to enter the Head of the Charles race in Boston and is trying to figure out how much money to raise. The entry fee is $\$ 250$ per boat for the first 10 boats and $\$ 175$ for each additional boat. Find the cost function $C(x)$ as a function of the number of boats the club enters $x$. Find the inverse function that will yield how many boats the club can enter as a function of how much money it will raise.

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 3, Problem 67

Instant Answer

Solved by Expert Suzanne W.

03/27/2022

Step 1

The cost function is defined as the total cost of entering $x$ boats into the race. The cost is $\$250$ per boat for the first 10 boats and $\$175$ for each additional boat. Therefore, we can write the cost function as follows: \[C(x) = \begin{cases} \$250x & Show more…

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Budget. The Richmond rowing club is planning to enter the Head of the Charles race in Boston and is trying to figure out how much money to raise. The entry fee is $\$ 250$ per boat for the first 10 boats and $\$ 175$ for each additional boat. Find the cost function $C(x)$ as a function of the number of boats the club enters $x$. Find the inverse function that will yield how many boats the club can enter as a function of how much money it will raise.

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Key Concepts

Piecewise Functions

Piecewise functions are used to represent situations where different rules apply to different intervals of the domain. They allow the construction of a model by defining separate expressions for different segments, such as tiered pricing structures where initial quantities are charged at one rate and additional quantities at a different rate.

Inverse Functions

Inverse functions reverse the input-output relationship of a function. They are used to determine the necessary input that gives a specific output, which is particularly useful in budget calculations where one needs to determine the number of units or entries possible with a given amount of money.

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