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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.

Sagot :

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:

[tex]P(t)=P_0\cdot(1+r)^t[/tex]

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:

[tex]\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}[/tex]

Answer: the population after 11 years will be 379660.

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