Question

Hello, what I guess I might want to understand is where to plug in the certain numbers/variables I am given. thank you

Answer 1

The given equation to get the accumulated amount is

`\begin{gathered} A=Pe^(rt) \\ \text{Where r = rate = 10\%}=(10)/(100)=\text{ 0}.1 \\ t\text{ = time in years} \\ P\text{= Amount invested}=\text{ \$6000} \\ A=\text{ Accumulated amount = 2 }*6000\text{ = \$12000 } \end{gathered}`

Therefore, by substituting in these values, t will be given as

`\begin{gathered} 12000\text{ = 6000}* e^(0.1* t) \\ (12000)/(6000)=e^(0.1t) \\ 2=e^(0.1t) \\ \ln \text{ 2 = 0.1t} \\ 0.6931471806=0.1t \\ t\text{ =}(0.6931471806)/(0.1) \\ t\text{ = }6.931471806 \\ t\approx6.9\text{ years to 1 decimal place} \end{gathered}`

t approximately = 6.9 years to 1 decimal place.