Solve the Problem. -A Patient Takes 100 Mg of Medication Every 24 Hours

Multiple Choice

Solve the problem.
-A patient takes 100 mg of medication every 24 hours. 80% of the medication in the blood is eliminated every 24 hours.

a. Let d_n equal the amount of medication (in mg) in the blood stream after n doses, where d₁ = 100. Find a recurrence relation for d_n .
b. Show that (d_n) is monotonic and bounded, and therefore converges.
c. Find the limit of the sequence. What is the physical meaning of this limit?

A) a. d_n + 1 = 0.2 d_n + 100, d₁ d₁ = 100
b. d_n satisfies 0 ≤ d_n ≤ 125 for n ≥ 1 and its terms are increasing in size.
c. 125; in the long run there will be approximately 125 mg of medication in the blood.

B) a. d_n + 1 = 0.8 d_n + 100, d₁ = 100
b. d_n satisfies 0 ≤ d_n ≤ 150 for n ≥ 1 and its terms are increasing in size.
c. 150; in the long run there will be approximately 150 mg of medication in the blood.


C) a. d_n + 1 = 0.2 d_n + 100, d₁ = 100
b. d_n satisfies 0 ≤ d_n ≤ 150 for n ≥ 1 and its terms are increasing in size.
c. 150; in the long run there will be approximately 150 mg of medication in the blood.

D) a. d_n + 1 = 0.8d_n + 100, d₁ = 100
b. d_n satisfies 0 ≤ d_n ≤ 125 for n ≥ 1 and its terms are increasing in size.
c. 125; in the long run there will be approximately 125 mg of medication in the blood.