Question

The town of Madison has a population of 25000. the population is increasing by a factor of 1.12 each year.

write a function that gives the population P(t) in Madison t years from now

P(t)=

Answer 1

`P(t) = 25000 \cdot (1.12)^t`

Explanation:

An exponential function is given by:

`y = ab^x`

where,

y is the amount after t years.

a is the initial amount

b is the growth factor.

As per the statement:

The town of Madison has a population of 25000.

⇒a = 25000

and the population is increasing by a factor of 1.12 each year.

⇒ b = 1.12

then by definition we have;

`P(t) = 25000 \cdot (1.12)^t`

where, P(t) is the population in t years from now.

Therefore, a function that gives the population P(t) in Madison t years from now is,
`P(t) = 25000 \cdot (1.12)^t`