Solve the Problem $A _ { 0 }$ Of the Drug in the Bloodstream at the Time of Treats

Multiple Choice

Solve the problem.
-The attending physician in an emergency room treats an unconscious patient suspected of a drug overdose. The physician does not know the initial concentration $A _ { 0 }$ of the drug in the bloodstream at the time of injection. However, the physician knows that after $3 \mathrm { hr }$ , the drug concentration in the blood is $0.75 \mu \mathrm { g } / \mathrm { dL }$ and after $4 \mathrm { hr }$ , the concentration is $0.719 \mu \mathrm { g } / \mathrm { dL }$ . The model $A ( t ) = A _ { 0 } \mathrm { e } ^ { - k t }$ represents the drug concentration $A ( t )$ (in $\mu \mathrm { g } / \mathrm { dL } )$ in the bloodstream $t$ hours after injection. The value of $k$ is a constant related to the rate at which the drug is removed by the body.

A) a. $0.75 = A _ { 0 } \mathrm { e } ^ { 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { 4 t }$
c. $k = 0.042$
B) a. $0.75 = A _ { 0 } \mathrm { e } ^ { - 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { - 4 t }$
c. $k = 0.618$
C) a. $0.75 = A _ { 0 } \mathrm { e } ^ { - 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { - 4 t }$
c. $k = 0.042$
D) a. $0.75 = A _ { 0 } \mathrm { e } ^ { 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { 4 t }$
c. $k = 0.618$