Need help with a growth problem

Question

Immediately following an injection, the concentration of a drug in the bloodstream is 200 milligrams per milliliter. After t hours, the concentration is 75% of the level of the previous hour.

 

(a) Find a model for C(t), the concentration of the drug after t hours.

 

C(t) =

 

(b) Determine the concentration of the drug after 4 hours. (Round your answer to the nearest whole number.)

milligrams per milliliter

Answer 1

PROBLEM

 

Need help with a growth problem
Immediately following an injection, the concentration of a drug in the bloodstream is 200 milligrams per milliliter. After t hours, the concentration is 75% of the level of the previous hour.

(a) Find a model for C(t), the concentration of the drug after t hours.

C(t) =

(b) Determine the concentration of the drug after 4 hours. (Round your answer to the nearest whole number.)
milligrams per milliliter

 

SOLUTION

 

(a) Find a model for C(t), the concentration of the drug after t hours.

C(t) = 200(3/4)^t

(b) Determine the concentration of the drug after 4 hours. (Round your answer to the nearest whole number.)
milligrams per milliliter

 

C(4) = 200(3/4)⁴

 

C(4) = 200(3⁴/4⁴)

 

C(4) = 200(81/256)

 

C(4) = 63.28125 mg/ml

 

C(4) ≈ 63 mg/ml