Thread: Problem with exponential function and logs

Hey, I have run aground on what im sure is a fairly simple logarithmic problem. Any help would be appreciated.
How would I go about solving a combination exponential and logarithmic problem such as this one:

Population of a city is observed as growing according to function P(t) = p0e^kt where the population has doubled after the first 30 years

- Find k
- By what factor will original population have grown after 120 years...

I thought to find k it was an application of ln. But im not sure what numbers i should be substituting into the exponential formula and where.
Please help!
Thanks

Hi thinkpol , welcome to MHF.
Population doubles in 30 years. So
P/Po = 2 = e^kt
Take log on both sides.
ln2 = 30*k.
Using calculator find ln2 and hence find k.

sa-ri-ga-ma

Im confused

so after i take:

ln2 = 30*k

do i simply divide ie

ln2/30 = k

?

Thanks for all the help

Is the correct value for k 0.023?

Originally Posted by thinkpol

sa-ri-ga-ma

Im confused

so after i take:

ln2 = 30*k

do i simply divide ie

ln2/30 = k

?

Thanks for all the help

Your value is correct.