Chapter 1.3, Problem 31E

To determine

To find: The number of bacteria in the colony at the end of 24 hours.

Answer to Problem 31E

The number of bacteria in the colony after 24 hours is $2.815\times {10}^{14}$ bacteria.

Explanation of Solution

Given information: The colony of bacteria starts with $1$ bacteria and doubles in every half hour.

Calculation:

As the bacteria doubles in every half hour, so $n$ is replaced with $2t$ in the exponential function.

The exponential function for the number of bacteria is given by:

  $\begin{array}{c}y=y_0{a}^n\\ y=1\times 2^{2t}\\ y=2^{2t}\end{array}$

Substitute $24$ for $t$ in the exponential formula.

  $\begin{array}{c}y=2^{2t}\\ y=2^{2\times 24}\\ y=2^{48}\end{array}$

Use the calculator for the value of $2^{48}$ . Press “ON” button and enter the keystrokes as given below:

  $\boxed{2}\boxed{^}\boxed{48}$

The value of $2^{48}$ is $2.815\times {10}^{14}$ .

Therefore, the number of bacteria in the colony after 24 hours is $2.815\times {10}^{14}$ bacteria.