Question

the amount of a medication remaining in patients bloodstreams was monitored over the course of two days. the equation y = 400(0.72)^x models the predicted number of milligrams, y, remaining x hours after taking the medication. interpret the percent rate of change in the context of the problem. the medication is predicted to lose 72 milligrams each hour after taking it. the medication is predicted to lose 28 milligrams each hour after taking it. the medication is predicted to lose about 72% of its quantity each hour after taking it. the medication is predicted to lose about 28% of its quantity each hour after taking it.

Explanation:

Step1: Identify the exponential - decay formula form

The general form of an exponential - decay formula is $y = a(1 - r)^x$, where $a$ is the initial amount, $r$ is the rate of decay, and $x$ is the number of time - intervals. In the given equation $y = 400(0.72)^x$, the base of the exponential function is $b = 0.72$.

Step2: Determine the rate of change

The rate of decay $r$ can be found from the base $b$ of the exponential function. If $b=1 - r$, then $r = 1 - b$. Here, $b = 0.72$, so $r=1 - 0.72=0.28$ or $28\%$. This means the medication is predicted to lose about $28\%$ of its quantity each hour after taking it.

Answer:

The medication is predicted to lose about $28\%$ of its quantity each hour after taking it.