Austin consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Austin's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Austin's body is 0.2785.

a. What is the 5-hour growth/decay factor for the number of mg of caffeine in Zach's body?

b. What is the 1-hour growth/decay factor for the number of mg of caffeine in Zach's body?

Question

Mathematics

Xander Richard

3 June, 09:10

Austin consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Austin's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Austin's body is 0.2785.

a. What is the 5-hour growth/decay factor for the number of mg of caffeine in Zach's body?

b. What is the 1-hour growth/decay factor for the number of mg of caffeine in Zach's body?

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Answers (1)

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Alyssa Guzman · Answer 1

5-hour: 0.5277 1-hour: 0.8800

Step-by-step explanation:

The decay factor for time t can be written as ...

0.2785^ (t/10)

Then the 5-hour decay factor is ...

0.2785^ (5/10) ≈ 0.5277

and the 1-hour decay factor is ...

0.2785^ (1/10) ≈ 0.8800