Question

I'm having an issue with the middle part of the logarithmic equation

Answer 1

The obtained function is :

`A=5500e^(0.07t)`

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 :

`\begin{gathered} 14500=5500e^(0.07t) \\ \Rightarrow(14500)/(5500)=e^(0.07t) \\ \Rightarrow\ln (14500)/(5500)=0.07t \\ \Rightarrow t=(\ln (14500)/(5500))/(0.07) \\ \Rightarrow t=13.849 \end{gathered}`

Rounded to 2 decimal places, the value of t will be :

`t=13.85\text{years}`

For the next question, the value of t when the amount is doubled :

`\begin{gathered} 2(5500)=5500e^(0.07t) \\ 2=e^(0.07t) \\ \ln 2=0.07t \\ t=(\ln 2)/(0.07) \\ t=9.902 \end{gathered}`

The answer is 9.90 years