Q 86 - Calculus

Question

Use the result of Example $7$ to approximate the levels of the drug Excellent´e during the first week, assuming the dosages and decay rates in Exercises $86-88$.

$L_1=200, p=50$.

Step-by-Step Solution

Answer

For $L_1=200, p=50$,  approximate level's of drug during the first week are as following :-

 $L_1=200,L_2=300,L_3=350,L_4=375,L_5=388,L_6=394 and L_7=397$.

Step 1. Given Information

We have given that :-

$L_1=200, p=50$

By using the result of example $7$ we have to approximate the drug Excellent'e during the first week.

Step 2. Approximate level's of drug during the first week.

We have $L_1=200,p=50$.

In example $7$, we find the following result :-

$L_1=D and L_{k+1}=\left(1-\frac{p}{100}\right)L_k+D for k\ge 1$

By using this result we have the following :-

$$\begin{gathered} L_2=\left(1-\frac{50}{100}\right)200+200 \\ \Rightarrow L_2=300 \end{gathered}$$

$$\begin{gathered} L_3=\left(1-\frac{50}{100}\right)300+200 \\ \Rightarrow L_3=350 \end{gathered}$$

$$\begin{gathered} L_4=\left(1-\frac{50}{100}\right)350+200 \\ \Rightarrow L_4=375 \end{gathered}$$

$$\begin{gathered} L_5=\left(1-\frac{50}{100}\right)375+200 \\ \Rightarrow L_5=387.5\approx 388 \end{gathered}$$

$$\begin{gathered} L_6=\left(1-\frac{50}{100}\right)388+200 \\ \Rightarrow L_6=394 \end{gathered}$$

and

$$\begin{gathered} L_7=\left(1-\frac{50}{100}\right)394+200 \\ \Rightarrow L_7=397 \end{gathered}$$