Problem
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 patient's body will decrease by a factor of $\frac{1}{3}$ each hour. Write an exponential equation in the form $y=a(b)^{x}$ that can model the amount of medication, $y$, remaining in the patient's body after $x$ hours. Use whole numbers, decimals, or simplified fractions for the values of $a$ and $b$. \[ y= \] Submit Work it out
Solution
Step 1 ：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 patient's body will decrease by a factor of $\frac{1}{3}$ each hour.
Step 2 ：Write an exponential equation in the form $y=a(b)^{x}$ that can model the amount of medication, $y$, remaining in the patient's body after $x$ hours.
Step 3 ：Use whole numbers, decimals, or simplified fractions for the values of $a$ and $b$.
Step 4 ：Final Answer: $\boxed{y=1.8\left(\frac{1}{3}\right)^{x}}$
