Question

The population of a city after t years is given by P(t) = 13,518e^0.041t, where t O corresponds to the current year.How many years from the current year will it take for the population of the city to reach 55,000?Round to the nearest hundredth of a year.In approximatelyyears the population of the city will reach 55,000.

Answer 1

1) Gathering the data

`\begin{gathered} P(t)=\text{ 13,158 }*10^(0.041t) \\ t_0=Current\text{ year} \\ \end{gathered}`

2) To find how many years from the current year will it take, let's plug into that equation:

`\begin{gathered} P(t)=\text{ 13,158 }* e^(0.041t) \\ 55,000=13158* e^(0.041t) \\ (55000)/(13158)=(13518)/(13518)* e^(0.041t)^{} \\ 4.1799=e^(0.041t)^{} \\ \ln (4.1799)\text{ =}\ln (e^(0.041t)) \\ 1.4302=0.041t \\ t=34.88\cong35 \end{gathered}`

3) So approximately 35 years from the current year.