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 d 1 = 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, d 1 d 1 = 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, d 1 = 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, d 1 = 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, d 1 = 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.

Question

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 d 1 = 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, d 1 d 1 = 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, d 1 = 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, d 1 = 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,  d 1 = 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.

Quizplus · Accepted Answer

The Answer of 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 d 1 = 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, d 1 d 1 = 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, d 1 = 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, d 1 = 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,  d 1 = 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.

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