Question

b. how many milligrams are in the bloodstream after 3 hours? please show an exact answer, as well as estimated to whole milligram.

d(3)=35e^{-0.3(3)}

Explanation:

Step1: Calculate the exponent

First, calculate the exponent \(-0.3\times3=- 0.9\).
So, \(D(3) = 35e^{-0.9}\).

Step2: Calculate the exact value

We know that \(e^{-0.9}=\frac{1}{e^{0.9}}\). Using a calculator, \(e^{0.9}\approx2.4596\), then \(e^{-0.9}=\frac{1}{2.4596}\approx0.4066\).
Multiply by 35: \(D(3)=35\times0.4066 = 14.231\) (exact value).

Step3: Estimate to the whole - number

To estimate \(14.231\) to the whole number, we look at the decimal part. Since \(0.231<0.5\), we round down.

Answer:

The exact answer is \(14.231\) milligrams. The answer estimated to the whole milligram is \(14\) milligrams.