A patient receives 100 mg of a drug each morning in pill form, and every 24 hour

ID: 2982092 • Letter: A

Question

A patient receives 100 mg of a drug each morning in pill form, and every 24 hours the patient's

body processes 80% of the drug in the pill, leaving 20% of the drug in the body. The amount of the

drug in the patient's body right after the rst pill is taken is A(1) = 100 mg. 24 hours later, after

the second pill has been taken, the amount in the patient's body is A(2) = 100(0:2)+ 100 = 120 mg.

After 48 hours, right after the patient takes the third pill, the amount of the drug in the patient's

body is A(3) = (100(0:2))(0:2) + 100(0:2) + 100 = 124 mg.

a) What do you notice about the value of A(n) as n gets larger? Write your observation math-

ematically. Interpret this behavior in terms of the amount of drug in the body after a long

period of time.

A(n)=100*(1+.2+.2^2+.2^3.................)

=100*(1-(.2)^n/(1-.2)

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