After a certain medicine is ingested, its concentration in the bloodstream changes over time.
The relationship between the elapsed time, \( t \), in minutes, since the medicine was ingested, and its concentration in the bloodstream, \( C(t) \), in \( \mathrm{mg} / \mathrm{L} \), is modeled by the following function:
\[
C(t)=78 \cdot(0.62)^{t}
\]
Complete the following sentence about the percent change in the concentration of the medicine.
Every minute, \( \% \) of concentration is added to / subtracted from \( \vee \) the total concentration of the medicine in the bloodstream.
Answer
\( \% \ = \frac{78(0.62)^{(t+1)} - 78(0.62)^{t}}{78(0.62)^{t}} \times 100 = (0.62-1)\times 100 \)
Step 1 ：\( C(t+1) = 78(0.62)^{(t+1)} \)
Step 2 ：\( \% \ = \frac{C(t+1) - C(t)}{C(t)} \times 100 \)
Step 3 ：\( \% \ = \frac{78(0.62)^{(t+1)} - 78(0.62)^{t}}{78(0.62)^{t}} \times 100 = (0.62-1)\times 100 \)
