I really need some help with my math homework - it's on logarithmic and exponential <span title="graphs/equations/interest?">graphs/equations/interest...</span>

Question

When continously compounding, I need to sole for time with the equation P=Ce^rt

How do you solve for t?

If you take the log of both sides, what happens to the numbers?

Answer 1

This type of logarithmic/exponential problem involves a growth || decay model that exhibits the continuous compounding formula: P = Ce^r*t.  To solve for t, you would have to use the inverse operation of exponentiation, which is logarthimic operations.  Thus, by taking the log of both sides, you have t = log(P /C) / r.  That which happens is the disappearance of the number e.  When applying logarithmic operations on both sides of the equation, it becomes logP / C = loge^rt = log(P/C) = r*t loge = log(P/C) = r * t.  Thus, t = log(P/C) / r.

J.C

Answer 2

I believe you should actually use the natural log(ln) of each side because of the e.

ln(P)=ln(Ce^rt)=ln(C)+rt(ln(e))

ln(e)=1...if I&#039;m remembering correctly...

therefore

t=(ln(P)-ln(C))/r  or (ln(P/C))/r