Chapter 8, Problem 3STP

To determine

To find: The correct option to determine the number of bacteria after 2 hours.

Answer to Problem 3STP

The number of cells after 2 hours is $64$ and the correct option is D.

Explanation of Solution

Given:

The bacteria reproduces after every 20 minutes.

The cell at the beginning is 1.

Calculation:

Consider the formula for the number of bacteria is,

  $y=a{e}^{kt}$

Then, the number of bacteria after $20\text{minutes}$ is,

  $\begin{array}{l}2=1e^{k\left(20\right)}\\ k=e^{k\left(20\right)}\\ 0.693=20k\\ k=0.035\end{array}$

Then, the number of bacteria on food after 2 hours or 120 minutes is given by the formula,

  $\begin{array}{c}y=1e^{\left(0.035\right)120}\\ =64.07\\ \approx 64\end{array}$

Thus, the number of cells after 2 hours is $64$ and the correct option is D.