Question

For these problems, please show your algebraic work using logarithms. 1. Determine the doubling time for each situation listed below. a. A population is growing according to P = P_0e^0.2t b. A bank account is growing by 2.7% each year compounded annually.

Answer 1

Answer: We need to find the doubling time for population growth:

Population growth is given by

`P=P_oe^((0.2)t)`

Where:

`\begin{gathered} P\rightarrow\text{final} \\ P_o\rightarrow I\text{nitial} \end{gathered}`

For the population to double, it implies that:

`P=2P_o`

Therefore:

`(P)/(P_o)=(2P_o)/(P_o)=2=e^((0.2)t)`

Solving for time "t" gives:

`2=e^((0.2)t)\rightarrow\ln (2)=(0.2)t\rightarrow t=(\ln (2))/((0.2))=3.46u`