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Video: Writing an Exponential Expression to Represent an Exponential Growth Model

Kathryn Kingham

The number of bacteria in a laboratory quadruples every hour. There were initially 200 bacteria. Write an expression for 𝐵(𝑡), the number of bacteria 𝑡 hours after the initial measurement.

02:15

Video Transcript

The number of bacteria in a laboratory quadruples every hour. There were initially 200 bacteria. Write an expression for ๐ต of ๐‘ก, the number of bacteria ๐‘ก hours after the initial movement.

What is our question asking us to do? They want us to write an expression to help us calculate how many bacteria would grow compared to the hours that have passed. The number of bacteria in the laboratory quadruples every hour. Quadruples would mean itโ€™s multiplied by a factor of four. Letโ€™s make a chart.

On hour zero before we started, there were 200 bacteria in the lab. But that number quadrupled by the first hour. That means itโ€™s multiplied by a factor of four. 200 times four equals 800. And by the second hour, there were 3200 bacteria.

How would we write an expression to show this? We have our 200 that we started with. In the first hour, our 200 is multiplied by four. Another way to say that is four to the first power. In our second hour, the 200 is multiplied by four and then by four again, or by four squared. We could say 200 times four squared. Our exponent here will be the time in hours that the bacteria is growing. We could write 200 times four to the ๐‘ก power. This tells us to take the number of hours that the bacteria is in a lab, four to that power times 200 will equal the total number of bacterias.

Our expression for this is 200 times four to the ๐‘ก power.