Question

Suppose the population of a town is 8,200 and is growing 3% each year. Write an equation to model the population growth. Predict the population after 3 years. y = 8,200 ∙ 3x; about 8,960 people y = 3 ∙ 8,200x; about 73,800 people y = 8,200 ∙ 3x; about 221,400 people y = 8,200 ∙ 1.03x; about 8,960 people

Answer 1

Hi There!

Find the population in 3 years.

8,200 x 0.03 = 246

8,200 + 246 = 8,446

8,446 x 0.03 = 253.38

8,446 + 253.38 = 8,699.38

8,699.38 x 0.03 = 260.9814

8,699.38 + 260.9814 = 8,960.3614

Round: 8,960.3614 = 8,960

Answer: y = 8,200 ∙ 1.03x; about 8,960 people

Hope This Helps :)

Answer 2

Option 4th is correct

`y = 8200(1.03)^t`

about 8,960 people

Explanation:

Using the formula:

`y=a(1+r)^t` .....[1]

where

`a` is the initial population.

r is the growth rate in decimal

y is the population after t years.

As per the statement:

Suppose the population of a town is 8,200 and is growing 3% each year.

⇒
`a = 8200` and r = 3% = 0.03

Substitute the given values in [1] , we have;

`y = 8200(1+0.03)^t`

⇒
`y = 8200(1.03)^t` .....[2]

Now, we have to find the population after 3 years.

Put t = 3 years in [2] we have;

`y = 8200(1.03)^3`

⇒
`y = 8200 \cdot 1.092727`

⇒
`y =8960.3614`

Therefore, an equation to model the population growth is,

`y = 8200(1.03)^t` ; and

The population after 3 years about 8,960 people