# Math Help - logarhythms and exponential growth.

1. ## logarhythms and exponential growth.

Hi, I'm not really confident with logarhythms yet and I know that there is a way of solving this problem using them.

A bacteria divides every 20 minutes, so how many are there after 24 hours?

Is this formula relevant here:

2. Originally Posted by lame_monkey
Hi, I'm not really confident with logarhythms yet and I know that there is a way of solving this problem using them.

A bacteria divides every 20 minutes, so how many are there after 24 hours?

Is this formula relevant here:
No, does that even make sense?

It divides every 20 minutes, so:

$N=N_0 2^{.05t}$

3. colby there is no need for the constant term, it is just t in minutes over 20.

4. Originally Posted by lame_monkey
Hi, I'm not really confident with logarhythms yet and I know that there is a way of solving this problem using them.

A bacteria divides every 20 minutes, so how many are there after 24 hours?

Is this formula relevant here:
Let t be measured in hours. So $20\ min = \frac13\ h$

If t = 0 you have $N_0$ bacteria.
If $t = 20\ min = \frac13\ h$ you have $2 \cdot N_0$

Now you can calculate the constant k:

$2 \cdot N_0 = N_0 \cdot e^{k \cdot \frac13}$. Divide by $N_0$ and solve for k:

$2= e^{k \cdot \frac13}~\implies~\ln(2)=k \cdot \frac13~\implies~k=3\ln(2)$

And now plug in the time to calculate $N_{24}$:

$N_{24} = N_0 e^{3\ln(2) \cdot 24}~\approx~4.7224 \cdot 10^{21} \cdot N_0$

And that's a really big number.

5. Thanks, that was really helpful.

And I was able to follow it, which is always a good sign lol