Question

25,989 Learners found this answer helpful

elizabeth is a nurse, and she just administered 1.8 milliliters of medication to one of her patients. elizabeth knows that the amount of medication remaining in the patients body will decrease by $\frac{1}{3}$ each hour. write an exponential equation in the form $y = a(b)^x$ that can model the amount of medication, $y$, remaining in the patients body after $x$ hours. use whole numbers, decimals, or simplified fractions for the values of $a$ and $b$.

Explanation:

Step1: Identify the initial amount

The initial amount of medication administered is 1.8 milliliters, so $a = 1.8$.

Step2: Determine the decay factor

The amount of medication decreases by $\frac{1}{3}$ each hour. So the remaining fraction of medication each hour is $1-\frac{1}{3}=\frac{2}{3}$, and $b=\frac{2}{3}$.

Answer:

$y = 1.8(\frac{2}{3})^{x}$