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Sagot :
Given:
Function :
[tex]A=800e^{0.085t}[/tex]Initial deposit =$800
Annual interest rate =8.5%
[tex]A=A_0e^{rt}[/tex]Where,
[tex]\begin{gathered} A=\text{Amount after t time} \\ A_0=\text{Initial amount} \\ r=\text{interest rate} \\ t=\text{time} \end{gathered}[/tex][tex]\begin{gathered} r=\frac{8.5}{100} \\ r=0.085 \end{gathered}[/tex]When deposit is double of initial deposit .
[tex]\begin{gathered} 2\times800=800e^{0.085t} \\ \frac{2\times800}{800}=e^{0.085t} \\ 2=e^{0.085t} \\ \ln 2=\ln e^{0.085t} \\ 0.085t=0.69314 \\ t=\frac{0.69314}{0.085} \\ t=8.15 \end{gathered}[/tex]So after 8.15 year initial amount will be double.
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