Question

A town

has a population of 14000 and grows at 2.5% every year. What will be the
population after 5 years, to the nearest whole number?

Answer 1

The answers is 15840

Explanation:

\text{Exponential Functions:}

Exponential Functions:

y=ab^x

y=ab

x

a=\text{starting value = }14000

a=starting value = 14000

r=\text{rate = }2.5\% = 0.025

r=rate = 2.5%=0.025

\text{Exponential Growth:}

Exponential Growth:

b=1+r=1+0.025=1.025

b=1+r=1+0.025=1.025

\text{Write Exponential Function:}

Write Exponential Function:

y=14000(1.025)^x

y=14000(1.025)

x

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=14000(1.025)^{5}

y=14000(1.025)

5

y= 15839.71498

y=15839.71498

Evaluate

y\approx 15840

y≈15840

round