To determine the percent change in the concentration of the medicine in the bloodstream every minute, let's analyze the given model:
The concentration of the medicine at time [tex]\( t \)[/tex] minutes is modeled by the function
[tex]\[ C(t) = 78 \cdot (0.62)^t. \][/tex]
Every minute, the concentration of the medicine is multiplied by [tex]\( 0.62 \)[/tex]. This factor, [tex]\( 0.62 \)[/tex], represents 62% of the previous concentration, indicating that with each passing minute, 62% of the previous concentration remains.
To find how much of the concentration is lost every minute as a percentage:
1. Start by noting that if 62% remains, then the fraction lost is [tex]\(1 - 0.62\)[/tex].
2. The percentage change can be calculated as:
[tex]\[ \text{Percent change per minute} = (1 - 0.62) \times 100\% \][/tex]
[tex]\[ \text{Percent change per minute} = 0.38 \times 100\% \][/tex]
[tex]\[ \text{Percent change per minute} = 38\%. \][/tex]
Thus, every minute, [tex]\(38\%\)[/tex] of the concentration is subtracted from the total concentration of the medicine in the bloodstream. Therefore, the completed sentence is:
Every minute, [tex]\(38\%\)[/tex] of concentration is subtracted from the total concentration of the medicine in the bloodstream.
