[tex]A=Pe^{rt}[/tex]
A=$88,000
P=$70,586
r=9.8% (0.098)
[tex]88,000=70,586e^{(0.098)t}[/tex]
Divide both sides by 70,586:
[tex]\begin{gathered} \frac{88,000}{70,586}=\frac{70,586}{70,586}e^{(0.098)t} \\ \\ \frac{88,000}{70,586}=e^{(0.098)t} \end{gathered}[/tex]
Find ln of both sides:
[tex]\begin{gathered} \ln (\frac{88,000}{70,586})=\ln (e^{(0.098)t}) \\ \\ \ln (\frac{88,000}{70,586})=0.098t \end{gathered}[/tex]
Divide both sides by 0.098:
[tex]\begin{gathered} \frac{\ln (\frac{88,000}{70,586})}{0.098}=\frac{0.098}{0.098}t \\ \\ \frac{\ln(\frac{88,000}{70,586})}{0.098}=t \\ \\ \\ t=2.25 \end{gathered}[/tex]Then, t is 2.25 years
