The obtained function is :
[tex]A=5500e^{0.07t}[/tex]
The question for the 3rd part is, how long will it be to have $14500 in the account.
Substitute A = 14500 and solve for the value of t :
[tex]\begin{gathered} 14500=5500e^{0.07t} \\ \Rightarrow\frac{14500}{5500}=e^{0.07t} \\ \Rightarrow\ln \frac{14500}{5500}=0.07t \\ \Rightarrow t=\frac{\ln \frac{14500}{5500}}{0.07} \\ \Rightarrow t=13.849 \end{gathered}[/tex]
Rounded to 2 decimal places, the value of t will be :
[tex]t=13.85\text{years}[/tex]
For the next question, the value of t when the amount is doubled :
[tex]\begin{gathered} 2(5500)=5500e^{0.07t} \\ 2=e^{0.07t} \\ \ln 2=0.07t \\ t=\frac{\ln 2}{0.07} \\ t=9.902 \end{gathered}[/tex]
The answer is 9.90 years
