Question

Juwan consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Juan's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Juan's body is 0.2213. What is the 5-hour growth/decay factor for the number of mg of caffeine in Juwan's body

Answer 1

0.47

Step-by-step explanation:

The Growth/decay factor is a factor that determines how fast a process increase or decreases.

Calculations

Given 10 hrs decay/growth factor = 0.2213

5 hrs decay/growth factor x=?

To obtain the 5 hours decay/growth factor we have to obtain 1-hour decay/growth factor;

let x be the 1-hour growth/decay factor and we have the expression below;

`x^(10) = 0.2213`

`x = 0.2213^{(1)/(10) }`

x = 0.86

The one-hour growth/decay factor is 0.86

Now the 5-hours growth/decay will be;

`5 hr decay factor = (1 hour decay factor)^(5)`

`5 hr decay factor = (0.86)^(5)`

5 hours growth/decay factor = 0.47

Therefore, the five-hours growth/decay factor for the number of mg of caffeine in Juwan's body is 0.47