Chapter 7.7, Problem 6CYU

To determine

The amount of salary Mr. Acosta will earn in 7 years.

Answer to Problem 6CYU

The amount of salary of Mr. Acosta in 7 years is $ $\mathrm{37734.73.}$ .

Explanation of Solution

Given information:

Initial salary of Mr. Acosta is $34,000.

Growth rate of salary is 1.5%.

Time is 7 years.

Calculation:

We know the exponential function equation is given by $y=a\cdot b^t$ , where $a$ is initial value, b is the growth factor and t is time (in years).

Also $b=1+r$ where r is growth rate.

We have

Initial value ( a) = 34,000

Growth rate ( r) = 1.5% = 0.015

Growth factor ( b ) = $1+r$ = 1+ 0.015 = 1.015

Time ( t ) = 7 years

Plugging the value of a = 34000 , b = 1.015 and t = 7 in exponential function equation $y=a\cdot b^t$ .

  $y=34000\cdot {(1.015)}^7$

Simplify

  $y\approx 34000\cdot \left(1.10984491\right)$

  $y\approx 37734.73$

Therefore, the amount of salary of Mr. Acosta in 7 years is approximately $ $37734.73$ .