Question

the cost in dollars of renting a bicycle in pismo beach is a function of the number of hours the bike is rented. the relationship between both variables can be modeled as $c(t) = 4.5t + 10$.
a) find the value of $c(3)$. write a sentence to interpret your answer in the context of the problem.
b) solve the equation $c(t) = 41.5$. write a sentence to interpret your answer in the context of the problem.

Explanation:

Part (a)

Step1: Substitute \( t = 3 \) into \( C(t) \)

We have the function \( C(t)=4.5t + 10 \). To find \( C(3) \), we replace \( t \) with 3 in the function. So, \( C(3)=4.5\times3 + 10 \).

Step2: Calculate the value

First, calculate \( 4.5\times3 = 13.5 \). Then, add 10: \( 13.5+10 = 23.5 \).

Step1: Set up the equation

We know \( C(t)=4.5t + 10 \) and \( C(t) = 41.5 \). So, we set up the equation \( 4.5t+10 = 41.5 \).

Step2: Solve for \( t \)

Subtract 10 from both sides of the equation: \( 4.5t+10 - 10=41.5 - 10 \), which simplifies to \( 4.5t = 31.5 \). Then, divide both sides by 4.5: \( t=\frac{31.5}{4.5}=7 \).

Answer:

\( C(3)=23.5 \). This means that the cost of renting a bicycle for 3 hours in Pismo Beach is $23.5.

Part (b)