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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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sqdancefan

Answer:

  • 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

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