Question

Find the size of a bacterial population after 80 minutes Find the size of a bacterial population after 6 hours.

Answer 1

Notice that the size of the population of bacteria can be model as an exponential function, meaning:

`\begin{gathered} P=P_0(1+r)^t \\ wereP_0\text{ is the initial population, r is the rate of change and t is the number of times} \\ \text{that the rate is applied.} \end{gathered}`

Substituting P₀=1500, r=1, and t=80/30 we get:

`P=1500(1+1)^{(80)/(30)}=9524`

Therefore after 80 minutes, the population of bacterias will be 9524.

For the second question, substituting P₀=1500, r=1, and t=12 we get:

`\begin{gathered} P=1500(1+1)^(12)=6144000 \\ \text{Therefore after 6 hours, the population of bacterias will be 6144000} \end{gathered}`