Question

In 2009, the population of Mexico was about 111.2 million, and the exponential growth rate was 1.13% per year. a) Estimate the population in 2016. b) After how long will the population be 150 million?

Answer 1

the equation to use is\[P _{t}=P _{2009}(1+r)^{t}=111.2(1+0.0113)^{7}\]
where Pt is the population t years after 2009, P2009 is the population in 2009, t is the number of years after 2009 and r is the growth rate.

Answer 2

For part b)
\[150=111.2(1+0.0113)^{t}\]
where t is the number of years after 2009. Solve to find t.

Hint: Take logs of both sides to begin solving>

Answer 3

\[\ln (\frac{150}{111.2})=t \times \ln 1.0113\]
\[t=\frac{\ln \frac{150}{111.2}}{\ln 1.0113}=you\ can\ solve\]