Chapter 7.9, Problem 49PFA

To determine

What is the predicted population in 2030?

Answer to Problem 49PFA

The predicted population in 2030 is 8,295.

Explanation of Solution

Given information:

Population of a town in 2016 = 10,250.

Decay rate of population is 1.5% each year.

Calculation:

We know the exponential function equation is given by $y=a\cdot b^t$ , where a is the initial population, b is growth/decay factor of population and t is the number of years after 2016.

Also $b=1-r$ where r is decay rate.

Initial population $(a)$ = 10,250

Decay rate $(r)$ = 1.5%=0.015

Decay factor $(b)$ = $1-0.015=\mathrm{0.985.}$

Plugging the value of a and b in exponential function equation

  $y=a\cdot b^t$

  $y=10250\cdot {\left(0.985\right)}^t$ .

For year 2030 the value of t is

  $=2030-2016=14years.$

Now, plugging the value of t in $y=10250\cdot {\left(0.985\right)}^t$ equation.

  $y=10250\cdot {\left(0.985\right)}^{14}$

  $y\approx 8295$

Therefore, the predicted population in 2030 is approximately 8,295.