Question

A country’s population grows at a rate of 0.017 per year. In the year 2000, the population was 91 million. What is the predicted population in the year 2007?

Use at least two sentences explain how to calculate the predicted population and identify the variables in the equation P(t) = P0ekt

Answer 1

2007 Population = 2000 Population * (1 + rate)^years
2007 Population = 91,000,000 * (1.017)^7
2007 Population = 91,000,000 * 1.1252439082
2007 Population = 102,397,195

Answer 2

Hence, the population in the year 2007 is:

102.3972 million

Explanation:

It is given that:

A country’s population grows at a rate of 0.017 per year.

In the year 2000, the population was 91 million.

i.e. this situation could be modeled with the help of a population function P(t) as:

`P(t)=P_0(1+0.017)^t`

where P(t) represents the population of in t years.

`P_0` represents the initial population i.e. population in the year 2000.

i.e.
`P_0=91\ \text{million}`

Hence, the population in the year 2007 i.e. t=7 is:

`P(t)=91* (1.017)^7\ \text{million}\\\\P(t)=102.3972\ \text{million}`

Hence, the population in the year 2007 is:

102.3972 million