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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.

Respuesta :

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

Population growth is given by

[tex]P=P_oe^{(0.2)t}[/tex]

Where:

[tex]\begin{gathered} P\rightarrow\text{final} \\ P_o\rightarrow I\text{nitial} \end{gathered}[/tex]

For the population to double, it implies that:

[tex]P=2P_o[/tex]

Therefore:

[tex]\frac{P}{P_o}=\frac{2P_o}{P_o}=2=e^{(0.2)t}[/tex]

Solving for time "t" gives:

[tex]2=e^{(0.2)t}\rightarrow\ln (2)=(0.2)t\rightarrow t=\frac{\ln (2)}{(0.2)}=3.46u[/tex]