Question

The number of bacteria in a certain population increases according to a continuous exponential growth rate parameter of 5.4% per hour. How many hours does it take for the size of the sample to double? Round your answer to the nearest hundredth.

Answer 1

We can express the groth of the bacterias by the following expression:

`g(t)=A*(1.054)^t`

Where A is the initial amount of bacteria, we want to know how many hours we need to double the initial amount. So we want to solve:

`2* A=A*(1.054)^t`

Lets use natural logaritm to help to solve the question:

`2* A=A*(1.054)^t\rightarrow2=(1.054)^t\rightarrow\ln 2=\ln (1.054)^t\rightarrow\ln 2=t*\ln 1.054\rightarrow t=(\ln 2)/(\ln 1.054)\cong13.179594`

So, we need 13.18 hours to double our initial amount.