Question

The number of bacteria in a colony is growing exponentially.

How many bacteria were there at 7 P.M. that day?

Short answer

The population of bacteria at 7 P.M. that day is1011929.

Step-by-step solution

Step 1. Given Information.

Given, the number of bacteria in a colony is growing exponentially as below:

An exponential function to model the population y of bacteria x hours after 2 P.M. is $y=100{\left(2\sqrt{10}\right)}^x$

The number of bacteria that were there at 7 P.M. that day is to be determined.

Step 2. Explanation.

For 7 P.M.:

$\begin{array}{l}x=7-2\\ x=5\end{array}$

Plugging the value to in the equation:

$\begin{array}{l}y=100{\left(2\sqrt{10}\right)}^x\\ y=100{\left(2\sqrt{10}\right)}^5\\ y\approx 1011929\end{array}$

Step 3. Conclusion.

Hence the population of bacteria at 7 P.M. that day is 1011929.