a. Find a recurrence relation for the sequence that gives the amount of drug in the blood after the
nth dose, where .
A.
B.
C.
D.
b. Using a calculator, determine the limit of the sequence. In the long run, how much drug is in
the person’s blood? Confirm the result by finding the limit of the sequence directly. Select the correct
choice below and, if necessary, fill in the answer box to complete your choice.
A. The limit of the sequence is
B. The limit does not exist.

Ask by Greene Wagner. in the United States

Mar 15,2025

Question

a. Find a recurrence relation for the sequence that gives the amount of drug in the blood after the
nth dose, where .
A.
B.
C.
D.
b. Using a calculator, determine the limit of the sequence. In the long run, how much drug is in
the person’s blood? Confirm the result by finding the limit of the sequence directly. Select the correct
choice below and, if necessary, fill in the answer box to complete your choice.
A. The limit of the sequence is
B. The limit does not exist.

Ask by Greene Wagner. in the United States

Mar 15,2025

UpStudy AI · Accepted Answer

We begin by noting that at each step the amount of drug in the blood decreases by a factor of $$\frac{1}{2}$$ and a new 60 milligrams dose is added. Since the initial dose is given as
$$
d_1=60,
$$
after each subsequent dose the drug amount becomes half of the previous amount plus the new dose. This gives the recurrence relation

$$
d_{n+1}=\frac{1}{2}d_n+60.
$$

Thus, for part (a) the correct choice is D.

For part (b) we find the limit of the sequence. If the sequence converges to a limit $$L$$, then taking the limit on both sides of the recurrence relation yields

$$
L=\frac{1}{2}L+60.
$$

Subtract $$\frac{1}{2}L$$ from both sides:

$$
L-\frac{1}{2}L=60 \quad\Longrightarrow\quad \frac{1}{2}L=60.
$$

Multiply both sides by 2:

$$
L=120.
$$

Thus, the long‐term (steady state) amount of the drug in the person’s blood is 120 milligrams. Therefore, for part (b) the correct choice is:

A. The limit of the sequence is $$120$$.
The recurrence relation is $$ d_{n+1} = \frac{1}{2}d_n + 60 $$. The limit of the sequence is 120 milligrams.

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