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:
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 $\displaystyle 20\ min = \frac13\ h$
If t = 0 you have $\displaystyle N_0$ bacteria.
If $\displaystyle t = 20\ min = \frac13\ h$ you have $\displaystyle 2 \cdot N_0$
Now you can calculate the constant k:
$\displaystyle 2 \cdot N_0 = N_0 \cdot e^{k \cdot \frac13}$. Divide by $\displaystyle N_0$ and solve for k:
$\displaystyle 2= e^{k \cdot \frac13}~\implies~\ln(2)=k \cdot \frac13~\implies~k=3\ln(2)$
And now plug in the time to calculate $\displaystyle N_{24}$:
$\displaystyle N_{24} = N_0 e^{3\ln(2) \cdot 24}~\approx~4.7224 \cdot 10^{21} \cdot N_0$
And that's a really big number.