Ben consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722. What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, . We use this to find k.

Then

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

We have to find find A(5), as a function of A(0). So

The decay factor is:

1 - 0.8531 = 0.1469

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

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step-by-step explanation: