Find initial value and growth in exponential growth model

$\begingroup$

I was given two models each with specific time($t$) and end amount($P$). $100$ after $3$ hours and $400$ after $5$ hours. Using the exponential growth model I get these $100=Pe^{3r}$ and $400=Pe^{5r}$. I heard you are suppose to divide these two so after that I got this: 4$=Pe^{5/3}$. Then I did the natural log of both and got this $r=0.831774$. After words I have to find the the end amount but I have no Initial Amount($P$). Only the rate and time. Advice?

$\endgroup$ 2

1 Answer

$\begingroup$

$$100=Pe^{3r} \\400=Pe^{5r} \\ \implies 4 = e^{5r-3r}=e^{2r} \\ \implies r=\ln2\approx0.693$$ Substitute $r$ in any equation to get the $P$.

$\endgroup$ 1

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy