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After a certain medicine is ingested, its concentration in the bloodstream changes over time.

The relationship between the elapsed time, [tex]t[/tex], in minutes, since the medicine was ingested, and its concentration in the bloodstream, [tex]C(t)[/tex], in [tex]mg / L[/tex], is modeled by the following function:
[tex] C(t) = 78 \cdot (0.62)^t [/tex]

Complete the following sentence about the percent change in the concentration of the medicine.

Every minute, [tex]\square[/tex] [tex]\%[/tex] of concentration is added to / subtracted from the total concentration of the medicine in the bloodstream.

Sagot :

GinnyAnsweridn
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.
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