Question

Alan consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Alan's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Alan's body is 0.2265. What is the 5-hour growth/decay factor for the number of mg of caffeine in Alan's body?

Answer 1

The 5 hour growth/decay factor for the number of milli-grams of caffeine in Alan's body is 0.4759

Explanation:

We are given the following in the question:

Caffeine in Alan's body decreases exponentially.

10 hour delay factor = 0.2265

We have to calculate 5 hour delay factor of Alan's body.

Let b be 1 hour delay factor.

Then, we can write

`b^(10) = 0.2265\\\Rightarrow b = (0.2265)^{(1)/(10)}\\\Rightarrow b \approx 0.8619`

To calculate 5-hour growth/decay factor:

`=(b)^5\\=(0.8619)^5\\=0.4759`

Thus, the 5 hour growth/decay factor for the number of milli-grams of caffeine in Alan's body is 0.4759