Question

The amount (in milligrams) of a drug in a person's body following one dose is given

by an exponential decay function. Let () denote the amount of drug in the body at
time in hours after the dose was taken. In addition, suppose you know that (3) =
22.7 and (6) = 15.2.
a. Find a formula for in the form () =

, where you determine the values
of and exactly.
b. What is the size of the initial dose the person was given?
c. How much of the drug remains in the person's body 8 hours after the dose
was taken?
d. Estimate how long it will take until there is less than 1 mg of the drug
remaining in the body.
e. Compute the average rate of change of on the intervals [3,5],
[5,7], and [7,9]. Explain the meaning of the values you found, including
appropriate units. Write at least one additional sentence to explain any
overall trend(s) you observe in the average rate of change.

Answer 1

The formula for the amount of drug in the body at time t after the dose was taken is (t) = (22.7 / 9) * (t^2), where t is the time in hours.

Step-by-step explanation:

To find a formula for the amount of drug in the body at time t after the dose was taken, we can use the exponential decay function formula: (t) = (t₂√) * A, where A is the initial amount of the drug. Let's plug in the given values to find the equation: 22.7 = (3₂√) * A and 15.2 = (6₂√) * A. Simplifying these equations, we find that A = 22.7 / 9 and A = 15.2 / 36. Therefore, the formula for the amount of drug in the body at time t is: (t) = (22.7 / 9) * (t₂√), where t is the time in hours after the dose was taken.