Question

The population of a large city is gradually moving to outlying metropolitan areas with the decline predicted by the functional equation, . If represents the present population of 1 million and P is the predicted population in t years, what is an estimate of the city’s population five years from now? Use 2.718 for e.

Answer 1

Given:

The equation representing the prediction of decline in the population is,

`P=P_Pe^(-0.3t)`

Population=

`P_P=1000,000`

e=2.718.

t = 5 years.

Required:

To estimate city's population five years from now.

Step-by-step explanation:

We have the equation representing the prediction of decline in the population given by,

`P=P_Pe^(-0.3t)`

Substituting values, we get,

`\begin{gathered} P=(1000,000)*(2.718)^(-0.3*5) \\ \Rightarrow P=(1000,000)*\left(2.718\right)^(-1.5) \\ \Rightarrow P=223164 \end{gathered}`

Final Answer:

The city's population five years from now is estimated by the value

`P=223164`

Second option is correct.