Question

A town has a population of 18000 and grows at 2% every year. What will be the population after 12 years, to the nearest whole number?

Answer 1

8377

Explanation:

A town has a population of 5000 and grows at 3.5% every year. What will be the population after 15 years, to the nearest whole number?

\text{Exponential Functions:}

Exponential Functions:

y=ab^x

y=ab

x

a=\text{starting value = }5000

a=starting value = 5000

r=\text{rate = }3.5\% = 0.035

r=rate = 3.5%=0.035

\text{Exponential Growth:}

Exponential Growth:

b=1+r=1+0.035=1.035

b=1+r=1+0.035=1.035

\text{Write Exponential Function:}

Write Exponential Function:

y=5000(1.035)^x

y=5000(1.035)

x

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=5000(1.035)^{15}

y=5000(1.035)

15

y= 8376.74415

y=8376.74415

Evaluate

y\approx 8377

y≈8377

round

Answer 2

22,828

Explanation:

To solve this problem, we can use the exponential growth formula, which is:

`A = P(1+r)^t`

A = total amount

P = original amount

r = growth rate (decimal)

t = years

Before we plug in the values, don't forget to change 2% to its decimal form.

2% ->
`(2)/(100)` -> 0.02

Lets plug in the values:

`A=18,000(1+0.02)^(12)`

`A=22,828`

The population after 12 years will be 22,828.