Chapter 7.6, Problem 16P

A new car costs $15,000 to build in 2010. The company’s financial analysts expect costs to rise by $6\%$ per year for the 10 years they are planning to build the car. The cost to build the car can be modeled by the function $f(t)=15,000{(1.06)}^t,$

where $t$ is the number of years after 2010. How much will it cost the company to build the car in 2017?

To determine

To find the cost to build the car in 2017.

Answer to Problem 16P

$22,554.45

Explanation of Solution

Given:

The function $f\left(t\right)=15,000{\left(1.06\right)}^t$ models the cost to build the car, where $t$ is the number of years after 2010.

Calculation:

  $2017-2010=7$

So put $t=7$ in $f\left(t\right)=15,000{\left(1.06\right)}^t$ , we get

  $\begin{array}{l}f\left(7\right)=15,000{\left(1.06\right)}^7\\ =\$\text{22,554}\text{.4538848704}\\ \approx \$\text{22,554}\text{.45}\end{array}$

Hence it costs $22,554.45 to build the car in 2017.