Chapter 7.4, Problem 56E

(a)

To determine

To find: The equation for the model to determine the amount of second dose in the bloodstream.

Answer to Problem 56E

The model for the aspirin after one dose is $\frac{391\left(t-1\right)+0.112}{0.218{\left(t-1\right)}^4+0.991{\left(t-1\right)}^2+1}$ .

Explanation of Solution

Given:

The amount of aspirin in milligram is given by the equation,

  $A=\frac{391t+0.112}{0.218t^4+0.991t^2+1}$

The given graphs are shown in Figure 1

  

Figure1

Calculation:

Consider the expression for the amount of bloodstream in the blood is,

  $A=\frac{391t+0.112}{0.218t^4+0.991t^2+1}$

Then, the aspirin in the blood after one dose is obtained as,

  $A\left(t-1\right)=\frac{391\left(t-1\right)+0.112}{0.218{\left(t-1\right)}^4+0.991{\left(t-1\right)}^2+1}$

(b)

To determine

To find: The model for the total amount of aspirin in the bloodstream after the second dose is taken.

Answer to Problem 56E

The model for the aspirin after two dose is $A\left(t\right)=\frac{391\left(t-1\right)+0.112}{0.218{\left(t-1\right)}^4+0.991{\left(t-1\right)}^2+1}+\frac{391\left(t-1\right)+0.112}{0.218{\left(t-1\right)}^4+0.991{\left(t-1\right)}^2+1}$ .

Explanation of Solution

Consider the expression for the amount of bloodstream in the blood is,

  $A=\frac{391t+0.112}{0.218t^4+0.991t^2+1}$

Then, the aspirin in the blood after the second dose is obtained as,

  $A\left(t\right)=\frac{391\left(t-1\right)+0.112}{0.218{\left(t-1\right)}^4+0.991{\left(t-1\right)}^2+1}+\frac{391\left(t-1\right)+0.112}{0.218{\left(t-1\right)}^4+0.991{\left(t-1\right)}^2+1}$