Q 87 - 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 $86-88$.

$L_1=100, p=25$.

Step-by-Step Solution

Answer

For $L_1=100, p=25$,approximate level's of drug during the first week are as following :-

$L_1=100,L_2=175,L_3=231,L_4=273,L_5=305,L_6=329 and L_7=347$. 

Step 1. Given Information

We have given that :-

$L_1=100, p=25$.

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 $L_1=100,p=25$.

In example , 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 :- 

$$\begin{gathered} L_2=\left(1-\frac{25}{100}\right)100+100 \\ \Rightarrow L_2=175 \end{gathered}$$

$$\begin{gathered} L_3=\left(1-\frac{25}{100}\right)175+100 \\ \Rightarrow L_3=231.25\approx 231 \end{gathered}$$

$$\begin{gathered} L_4=\left(1-\frac{25}{100}\right)231+100 \\ \Rightarrow L_4=273.25\approx 273 \end{gathered}$$

$$\begin{gathered} L_5=\left(1-\frac{25}{100}\right)273+100 \\ \Rightarrow L_5=304.75\approx 305 \end{gathered}$$

$$\begin{gathered} L_6=\left(1-\frac{25}{100}\right)305+100 \\ \Rightarrow L_6=328.75\approx 329 \end{gathered}$$

and

$$\begin{gathered} L_7=\left(1-\frac{25}{100}\right)329+100 \\ \Rightarrow L_7=346.75\approx 347 \end{gathered}$$