Sergio consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Sergio's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Sergio's body is 0.2661.

What is the 5-Hour growth/decay factor for the number of mg of caffeine in Eric's body?

0.5158

Step-by-step explanation:

The exponential decay of a given material is used to describe the process by which a material decreases in size and amount over a specific period of time. The material will decay with respect to its decay factor. Therefore, if the 10-hour decay factor is approximately 0.2661, the 5-hour growth/decay factor will be: (0.2661) ^ (5/10) = (0.2661) ^0.5 = 0.5158.

0.5158

Step-by-step explanation:

Given, 10 hour Sergio's decay factor = 0.2661

First calculate for 1 hour decay factor

1 hour decay factor = (10 hour decay factor) ^1/10

= (0.2661) ^1/10

1 hour decay factor = 0.8760

Therefore to calculate for 5 hour decay factor

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

= (0.8760) ^5

= 0.5158