# Population growth using logarithims

## Homework Statement

A culture begins with 100,000 bacteria and grows to 125,000 bacteria after 20 min. What is the doubling period to the nearest minute?

## Homework Equations

Current=Original(rate)^time

## The Attempt at a Solution

I can get make the first part out. 125000=100000(rate)^2 I have a feeling its wrong but its as far as i can get.

## Answers and Replies

Char. Limit
Gold Member
Well, yeah. The doubling period is time, and it's supposed to be the thing you're solving for.

So would my rate be 2? if so then would this be right 120000=100000(2)^t
1.25=2^t
log1.25/log2=t?

What confuses me is when it says doubling period, is that time or the rate?

Char. Limit
Gold Member
Well, start with this:

The original is 100,000 and it changes to 125,000 in 20 minutes. So, first solve for the rate, then put in the rate to the equation 200,000=100,000(rate)^(time)

Well i can get this far but i cant get farther sorry.
125000=100000(rate)^20
125000/100000=r^20
log (125000/100000)=20log r

I don't know how to go farther, if r had a value and i was solving for time i would have no problem with this.

alrighhhht worked it out on my own :)

I figured, why log to find the rate, 20th root it.

125000/100000=r^20
(20th root) 1.25=r
r=1.01

200000=100000(1.01)^t
2=1.01^t
log 2/log1.01=t
t=62 minutes which is the answer in the back of my textbook. Thanks for setting me on the right path Char.Limit :D

Char. Limit
Gold Member
No problem. And it's true... roots are almost always easier than logs.