2. The function [tex]D(h) = 8e^{-0.3h}[/tex] can be used to find the number of milligrams [tex]D[/tex] of a certain drug that is in a patient's bloodstream [tex]h[/tex] hours after the drug has been administered.

a. How many milligrams will be present after 4 hours?

b. When the number of milligrams reaches 1, the drug is to be administered again. After how many hours will the drug need to be administered?

3. A radioactive isotope, selenium, used in the creation of medical images of the pancreas, has a half-life of 119.77 days. If 100 milligrams are given to a patient, how many milligrams are left after 20 days?

2.) a. To find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered, we can use the function D(h) = 8e^-0.3h.

If h = 4, then the number of milligrams of drug in the patient's bloodstream is:

D(4) = 8e^-0.3(4) = 2.56

Therefore, after 4 hours, there will be 2.56 milligrams of drug in the patient's bloodstream.

b. The drug needs to be administered again when the number of milligrams reaches 1. So, we need to solve the equation D(h) = 1.

8e^-0.3h = 1

e^-0.3h = 0.125

-0.3h = ln(0.125)

h = -3.01

Therefore, the drug needs to be administered again after 3.01 hours.

3.) A radioactive isotope, selenium, used in the creation of medical images of the pancreas, has a half-life of 119.77 days. If 100 milligrams are given to a patient, then after 20 days, the number of milligrams left is:

100 * (1/2)^(20/119.77) = 100 * (1/2)^(0.164) = 24.79

Therefore, after 20 days, there will be 24.79 milligrams of selenium left.

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