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

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

The function that gives the population P(t) in Madison t years from now is $\rm P(x)=25000(1.2)^t$.

Given

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

What is the function?

A relation or expression involving one or more variables:

Let  P(t) be the population in Madison t years from now.

Then,

The exponential population growth function is;

$\rm y=ab^x$

Where; y is the amount after t years, a is the initial amount, b is the growth factor.

Therefore,

The function that gives the population P(t) in Madison t years from now is;

$\rm P(x)=25000\times (1.2)^t\\\\P(x)=25000(1.2)^t$

Hence, the function that gives the population P(t) in Madison t years from now is $\rm P(x)=25000(1.2)^t$.

To know more about growth factors click the link given below.

https://brainly.com/question/11702440