Question

Finding the rate or time in a word problem on continuous exponential growth or decay

Answer 1

continuous exponential growth model

`A=Pe^(r\cdot t)`

since the size of the sample doubled:

A/P = 2

r = 8.5% = 0.085

e: eurler's number = 2.71828...

therefore,

`\begin{gathered} (A)/(P)=e^(r\cdot t) \\ 2=e^(0.085\cdot t) \end{gathered}`

apply the law of exponents

`\ln \mleft(2\mright)=0.085t`
`t=(\ln\left(2\right))/(0.085)`

So, t = 8.15467...

rounding to the nearest hundred

t = 8.15