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

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 tha class=

Respuesta :

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]

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