Chapter 7.7, Problem 15P

The town manager reports that revenue for a given year is $2.5 million. The budget director predicts that revenue will increase by $4\%$ per yr. If the director’s prediction holds true, how much revenue will the town have available 10 years from the date of the town manager’s report? Write an expression to represent the equivalent monthly increase in revenue.

To determine

To calculate: The town manager reports that revenue for the given year is $2.5 million. The budget director predicts that revenue will increase by 4% per year. If the director's prediction holds true, how much revenue the town will have available 10 years from the date of the town manager's report?

Answer to Problem 15P

$3.7 million.

Explanation of Solution

Given information:Initially revenue of town is $2.5 million and it will increase at the rate of 4% per year.

Calculation:To find the revenue after 10 years which increases constantly 4% per year, we can use compound interest method or we can use exponential growth function.

According to exponential growth function, we have

  $y=a*{\left(1+\frac{r}{100}\right)}^x$ , where

  $a=$ initial amount of revenue

  $r=$ rate of growth

  $x=$ time period in years

so, $y=2.5{\left(1+\frac{4}{100}\right)}^{10}$

  $y=2.5{\left(1.04\right)}^{10}$

  $y=3.7$

Hence after 10 years the revenue of town will be $3.7 million.