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.

Answer 1

P=8200(1.03)t P is the population after t years. t=3 P=8200(1.03)3=8960.3614=8960

Answer 2

• The exponential model is given by
  `Q=8200(1.03)^t`

• The population after 3 years is given by 8960

Explanation:

The exponential model is given by

`Q=A_0(1+r)^t`

Here, Q = final population, Q_0 = initial population, r = growth/decay rate, t = time

Now, we have been given

`Q_0=8200,r=3\%=0.03`

On substituting these values, the model is given by

`Q=8200(1+0.03)^t\\Q=8200(1.03)^t`

Now, the population after 3 years is given by

`Q=8200(1.03)^3\approx 8960`