The amount (in milligrams) of a drug in the body $t$ hours after taking the pill is given by \[ f(t)=65(0.70)^{t} \] (a) What is the initial dose given? (b) What percent of the drug leaves the body every hour? (c) What is the amount of drug left after 2 hours? Click here to enter answer
Solution
Step 1 ：Define the function \(f(t) = 65 \times (0.70)^t\), which represents the amount (in milligrams) of a drug in the body \(t\) hours after taking the pill.
Step 2 ：Calculate the initial dose given by evaluating the function at \(t = 0\). This gives \(f(0) = 65 \times (0.70)^0 = 65\). So, the initial dose given is \(\boxed{65}\) milligrams.
Step 3 ：Determine the percent of the drug that leaves the body every hour. This is given by \(100 - 0.70 \times 100 = 30\%\). So, \(\boxed{30\%}\) of the drug leaves the body every hour.
Step 4 ：Calculate the amount of drug left after 2 hours by evaluating the function at \(t = 2\). This gives \(f(2) = 65 \times (0.70)^2 \approx 31.85\). So, the amount of drug left after 2 hours is approximately \(\boxed{31.85}\) milligrams.
