Choose the one alternative that best completes the statement or answers the question.
-The amount of a certain drug in the bloodstream is modeled by the function $\mathrm { y } = \mathrm { y } _ { 0 } \mathrm { e } ^ { - 0.40 \mathrm { t } }$, where $\mathrm { y } _ { 0 }$ is the amount of the drug injected (in milligrams) and $t$ is the elapsed time (in hours). Suppose that 10 milligrams are injected at 10:00 A.M. If a second injection is to be administered when there is 1 milligram of the drug present in the bloodstream, approximately when should the next dose be given? Express your answer to the nearest quarter hour.
A) 5:45 P.M
B) $5 : 30$ P.M
C) $3 : 45$ P.M
D) $12 : 30$ P.M

Question

Quizplus · Accepted Answer

To find when the next dose should be given, we need to solve for $t$ when $y = 1$ milligram, given that $y_0 = 10$ milligrams. Substituting these values into the equation $y = y_0 e^{-0.40t}$, we get $1 = 10e^{-0.40t}$. Solving for $t$ gives $t \approx 5.75$ hours. Since the initial dose was at 10:00 A.M., adding 5.75 hours leads to approximately 3:45 P.M.

Choose the One Alternative That Best Completes the Statement or Answers