Question

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?

Answer 1

• 5-hour: 0.5277
• 1-hour: 0.8800

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