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 fro…

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asked Feb 4, 2019 222k views

1 Answer

Lexu · Answer 1 · 2019-02-08T13:42:36+0000

Answer:

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

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,
$P(t) = 25000 \cdot (1.12)^t$