Question

Suppose the population of a town is 2,700 and is growing 4% each year. A. Write an equation to model the population growth. B. Predict the population after 12 years. y = 2,700 • 4x; about 45,298,483,200 people y = 4 • 2,700x ; about 129,600 people y = 2,700 • 1.04x ; about 4,323 people y = 2,700 • 4x ; about 4,323 people

Answer 1

Equation to model the population growth is
`y = 2700(1.04)^(x)` and the population after 12 years is 4323 (Approx) .

Explanation:

The exponential increase function is given by

`y = a (1 + r)^(x)`

Where a is the initial value, r is the rate of interest in the decimal form and x is the time in years .

As given

Suppose the population of a town is 2,700 and is growing 4% each year.

a = 2700

4% is written in the decimal form .

`= (4)/(100)`

= 0.04

r = 0.04

Thus the equation becomes for population growth.

`y = 2700(1 + 0.04)^(x)`

`y = 2700(1.04)^(x)`

As given

x = 12 years

Put in the formula

`y = 2700(1.04)^(12)`

`y = 2700* 1.60103`

y = 4323 (Approx)

Therefore the population after 12 years is 4323 (Approx) .

Answer 2

Third option i.e. A.
`2700(1.04)^x` and B. About 4,323 people

Explanation:

We are given that,

Initial population of the town = 2,700

The rate of growth = 4% = 0.04

Part A: Since, the equation for the growth is given by,

Population growth =
`P(1+r)^x`, where P is the initial population, r is the rate of growth and x is the time period of growth.

We have, according to the question,

Population growth =
`2700(1+0.04)^x`

i.e. Population growth =
`2700(1.04)^x`

Thus, the equation for the population growth is
`2700(1.04)^x`.

Part B: Now, it is required to find the population after 12 years i.e. x= 12.

So, we have,

Population =
`2700(1.04)^x`

i.e. Population =
`2700(1.04)^(12)`

i.e. Population =
`2700* 1.601032`

i.e. Population = 4,323

Hence, the population after 12 years is 4,323 people.

Thus, the third option is correct.