Question

Adam is working in a lab testing bacteria populations. After starting out with a population of 390 bacteria, he observes the change in population and notices that the population quadruples every 20 minutes.Step 2 of 2 : Find the population after 1 hour. Round to the nearest bacterium.

Answer 1

The given information is:

The starting population of bacteria is 390.

The population quadruples every 20 minutes.

To find the equation of the population in terms of minutes, we can apply the following formula:

`P(t)=P_0\cdot4^{((t)/(20))}`

Where P0 is the starting population, the number 4 is because the population quadruples every 20 minutes (the 20 in the power is given by this), it is equal to 4 times the initial number, and t is the time in minutes.

If we replace the known values, we obtain:

`P(t)=390\cdot4^{((t)/(20))}`

To find the population after 1 hour, we need to convert 1 hour to minutes, and it is equal to 60 minutes, then we need to replace t=60 in the formula and solve:

`\begin{gathered} P(60)=390\cdot4^{((60)/(20))} \\ P(60)=390\cdot4^3 \\ P(60)=390\cdot64 \\ P(60)=24960\text{ bacterias} \end{gathered}`

Thus, after 1 hour there are 24960 bacterias.