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

Answer:

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

Step-by-step 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 .

$= \frac{4}{100}$

= 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

$y = 2700(1.04)^{12}$

$y = 2700\times 1.60103$

y = 4323 (Approx)

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

Answer 2

Answer:

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

Step-by-step 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 = $2700\times 1.601032$

i.e. Population = 4,323

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

Thus, the third option is correct.