Chapter 4.2, Problem 34E

(a)

To determine

The normal systolic pressure of a 25-year-old woman.

Answer to Problem 34E

114.5 millimeters of mercury

Explanation of Solution

Given information: Health: Normal systolic blood pressure is a function of age. For woman, the normal systolic pressure P in millimeters of mercury (mm Hg) is modeled by $P=0.01A^2+0.05A+107,$ where A is age in years.

Calculation:

Systolic pressure P in millimeters of mercury (mm Hg) is modeled by

  $P=0.01A^2+0.05A+107$

Where A is age in years

  $A=25\text{ years}$

The normal systolic pressure of a 25-year-old woman

  $\begin{array}{l}P=0.01{\left(25\right)}^2+0.05\left(25\right)+107\\ P=6.25+1.25+107\\ P=114.5\text{ millimeters of mercury}\end{array}$

The normal systolic pressure of a 25-year-old woman = 114.5 millimeters of mercury

(b)

To determine

The age of a woman whose normal systolic pressure is 125 mm Hg.

Answer to Problem 34E

Age of the woman is 40 years

Explanation of Solution

Given information: Health: Normal systolic blood pressure is a function of age. For woman, the normal systolic pressure P in millimeters of mercury (mm Hg) is modeled by $P=0.01A^2+0.05A+107,$ where A is age in years.

Calculation:

Systolic pressure P in millimeters of mercury (mm Hg) is modeled by

  $P=0.01A^2+0.05A+107$

Where A is age in years

P = 125 mm Hg

  $\begin{array}{l}125=0.01A^2+0.05A+107\\ 0.01A^2+0.05A-18=0\end{array}$

Multiply both sides with 100

  $A^2+5A-1800=0$

Factorize the equation

  $\begin{array}{l}\left(A-40\right)\left(A+45\right)=0\\ A=40\text{ or }A=-45\end{array}$

Age cannot have a negative value. So A = 40

Age of the woman is 40 years

(c)

To determine

To sketch: graph of the function and describe any change in normal systolic pressure as a woman gets older.

Answer to Problem 34E

Normal systolic pressure increases with the age of the women

Explanation of Solution

Given information: Health: Normal systolic blood pressure is a function of age. For woman, the normal systolic pressure P in millimeters of mercury (mm Hg) is modeled by $P=0.01A^2+0.05A+107,$ where A is age in years.

Calculation:

Normal systolic pressure is:

  $P=0.01A^2+0.05A+107$

The graph

  

From the graph it is clear that the systolic pressure increases with the age of the women.