Question

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

Answer 1

Answer:

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

Step-by-step 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, $P(t) = 25000 \cdot (1.12)^t$

Answer 2

Answer:

P(t)=25000(1.12)^t

Step-by-step explanation:

If we start with the initial population size, 25,000 people, and keep multiplying by 1.12 this function gives us the population of Madison t years from now: P(t)=25000(1.12)^t