Question

question 3 (multiple choice worth 2 points) (exponential models mc) the amount of a medication remaining in patients bloodstreams was monitored over the course of two days. the equation ŷ = 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: Recall exponential - decay formula

The general form of an exponential - decay function 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 function $\hat{y}=400(0.72)^x$, we can rewrite it in the general form. Here, $a = 400$ and the base of the exponential function is $b=0.72$.

Step2: Identify the rate of change

The rate of decay $r$ is found using the formula $b = 1 - r$. If $b = 0.72$, then $r=1 - 0.72=0.28$ or 28%. This means that the amount of medication in the patient's bloodstream is decreasing by 28% each hour.

Answer:

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