I need help finding the correct formula after finding the doubling time and continuous percentage. I got the doubling time of 24 days and the continuous percentage of 2.89%.

Question

Homework asking use the doubling time to find the continuous percent growth rate and give a formula of the function.

For the formula it says round all coefficients to 4 decimal places if required.

I attempted to do it but I don't think my method is working

I put P = ln(2) / 24

Answer 1

I don't know what the original problem was, but if the doubling time is 24 days, the formula for the amount present after t days is

A(t) = Ao * 2^(t/24)

Since 2 = e^ln2, that is equivalent to

A(t) = Ao * e^(ln2/24 t)