Question

Bobby is working in a lab testing bacteria populations. After starting out with a population of 282 bacteria, he observes the change in population and notices that the population quadruples every 39 minutes.Step 1 of 2 : Find the equation for the population P in terms of time t in minutes. Round values to three decimal places.Answer

Answer 1

Given that the population quadruples every 39 minutes, you can determine that this bacteria population has Exponential Growth.

By definition, an Exponential Equation as this form:

$y=ab^t$

Where "a" is the initial amount, "b" is the base, and "t" is the time period.

In this case, you know that:

$\begin{gathered} a=282 \\ b=4 \\ y=P \end{gathered}$

Therefore, since you need to express the time "t" in minutes:

$t=\frac{t}{39}$

Now you can write the following equation to model the situation:

$P=282\cdot4^{\frac{t}{39}}$