Okay, here we have this:
Considering the provided information we obtain the following:
a)
Replacing in the Compound Interest formula we obtain the following:
[tex]\begin{gathered} A(t)=Pe^{rt} \\ A(t)=16065e^{0.066t} \end{gathered}[/tex]b)
After 1 year (t=1):
[tex]\begin{gathered} A(1)=16065e^{0.066(1)} \\ A(1)\approx17,161.06 \end{gathered}[/tex]We obtain that after one year the balance is aproximately $17,161.06.
After 2 years (t=2):
[tex]\begin{gathered} A(2)=16065e^{0.066(2)} \\ A(2)=18331.90 \end{gathered}[/tex]We obtain that after two years the balance is aproximately $18,331.90
After 5 years (t=5):
[tex]\begin{gathered} A(5)=16065e^{0.066(5)} \\ A(5)=$22,345.90$ \end{gathered}[/tex]We obtain that after five years the balance is aproximately $22,345.90.
After 10 years (t=10):
[tex]\begin{gathered} A(10)=16065e^{0.066(10)} \\ A(10)=$31,082.44$ \end{gathered}[/tex]We obtain that after ten years the balance is aproximately $31,082.44.
c)
In this case the doubling time will be when she has double what she initially had, that is: $16,065*2=$32130, replacing in the formula:
[tex]32130=16065e^{0.066t}[/tex]Let's solve for t:
[tex]\begin{gathered} 32130=16065e^{0.066t} \\ 16065e^{\mleft\{0.066t\mright\}}=32130 \\ \frac{16065e^{0.066t}}{16065}=\frac{32130}{16065} \\ e^{\mleft\{0.066t\mright\}}=2 \\ 0.066t=\ln \mleft(2\mright) \\ t=\frac{\ln\left(2\right)}{0.066} \\ t\approx10.502years \end{gathered}[/tex]Finally we obtain that the doubling time is approximately 10.502 years or about 10 years 6 months.
