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:
[tex]y=ab^t[/tex]
Where "a" is the initial amount, "b" is the base, and "t" is the time period.
In this case, you know that:
[tex]\begin{gathered} a=282 \\ b=4 \\ y=P \end{gathered}[/tex]
Therefore, since you need to express the time "t" in minutes:
[tex]t=\frac{t}{39}[/tex]
Now you can write the following equation to model the situation:
[tex]P=282\cdot4^{\frac{t}{39}}[/tex]