Question

A certain population of bacteria demonstrates exponential growth doubles in size every 4 days. How long will it take the population to triple in size?

Answer 1

Answer:

In 6.4 days the size of the population will be tripled.

Step-by-step explanation:

Let the equation be $A=Pe^{rt}$

Given that the population doubles every 4 days.

It means, A becomes 2P in 4 days.

$2P=Pe^{r(4)}\\\\2=e^{4r}\\\\\ln2=4r\\\\r=\frac{1}{4}\ln2\\\\r\approx 0.1733$

Now, we have to find time t, when A becomes 3P.

$3P=Pe^{0.1733t}\\\\3=e^{0.1733t}\\\\\ln3=0.1733t\\\\t=\frac{1}{0.1733}\ln3\\\\t\approx6.4$

Therefore, in 6.4 days the size of the population will be tripled.