Question

A biologist discovered a new species of bacteria. He puts a certain amount of the bacteria into petri dish at t = 0 hours. The amount of bacteria in the petri dish can be modeled by P(t)=165e^0.600t. a) find and interpret P(0)b) according to the model, what will the population of bacteria be after 5 hours and 10 hours?

Answer 1

We are given an equation to model the population of a bacteria after t hours with the following form:

$P(t)=165e^{0.06t}$

By replacing 0 for t we determine the population of bacteria at the begining of the experiment, then we get:

$\begin{gathered} P(0)=165e^{0.06\times0} \\ P(0)=165e^0 \\ P(0)=165\times1 \\ P(0)=165 \end{gathered}$

Then P(0) = 165, this means that at the begining of the experiments there were 165 bacterias.

In order to determine the population after 5 hours we just have to replace 5 for t into the model, then we get:

$\begin{gathered} P(5)=165e^{0.06\times5} \\ P(5)=165\times1.35=222 \end{gathered}$

Then, the population of bacteria after 5 hours will be 222. Similarly for 10 hours:

$\begin{gathered} P(10)=165e^{0.06\times10} \\ P(10)=300 \end{gathered}$

Then the population of bacteria after 10 hours will be 300