Question

Suppose a city with a population of 200,000 has been growing at a rate of 6% per year. If this rate continues, find the population of this city in 11 years.

Answer 1

We have a population of 200,000 people that increase by 6%. We have to calculate the population after 11 years.

We can model the population at year t as:

`P(t)=P_0\cdot(1+r)^t`

where P0 is the population of 200,000 and r is the growth rate r = 0.06.

Wecan calculate the population after 11 years as:

`\begin{gathered} P(11)=P_0\cdot(1+r)^(11) \\ P(11)=200000\cdot(1+0.06)^(11) \\ P(11)=200000\cdot1.06^(11) \\ P(11)\approx200000\cdot1.8983 \\ P(11)\approx379660 \end{gathered}`

Answer: the population after 11 years will be 379660.