Question

Finding the time given an exponential function with base e that models a real world situation

Answer 1

Answer:

The time needed before the patient is to be injected again is;

$h=1.7\text{ hours}$

Explanation:

Given that the function that can model the exponential relationship between time (h) and the milligram of a drug in a patient's bloodstream D(h) is;

$D(h)=50e^{-0.25h}$

we want to calculate the time in hours before a patient is to be injected again when;

$D(h)=33$

Substituting in the given function, we have;

$\begin{gathered} D(h)=50e^{-0.25h} \\ 33=50e^{-0.25h} \end{gathered}$

taking the natural logarithm of the function;

$\begin{gathered} 33=50e^{-0.25h} \\ ln33=ln50-0.25h \\ 0.25h=ln50-ln33 \\ h=\frac{ln50-ln33}{0.25} \\ h=1.66 \\ h=1.7\text{ hours} \end{gathered}$

Therefore, the time needed before the patient is to be injected again is;

$h=1.7\text{hours}$