A person's systolic blood pressure, which is measured in millimeters of mercury $(\mathrm{mm} \mathrm{Hg})$ , depends on a person's age, in years. The equation: $\newline$ $P=0.006 y^{2}-0.03 y+122$ $\newline$ gives a person's blood pressure, $P$ , at age $y$ years. $\newline$ A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age $44$ years.___ $\newline$ B.) If a person's systolic pressure is $130.86 \mathrm{~mm} \mathrm{Hg}$ , what is their age (rounded to the nearest whole year)?_

Full solution

Q. A person's systolic blood pressure, which is measured in millimeters of mercury

(\mathrm{mm} \mathrm{Hg})

, depends on a person's age, in years. The equation:

\newline

P=0.006 y^{2}-0.03 y+122

\newline

gives a person's blood pressure,

P

, at age

y

years.

\newline

A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age

44

years._________

\newline

B.) If a person's systolic pressure is

130.86 \mathrm{~mm} \mathrm{Hg}

, what is their age (rounded to the nearest whole year)?_______

Calculate Systolic Pressure: A.) Calculate the systolic pressure for a person aged $44$ years. $\newline$ Substitute $y = 44$ into the equation $P = 0.006y^2 - 0.03y + 122$ . $\newline$ $P = 0.006(44)^2 - 0.03(44) + 122$ $\newline$ $P = 0.006(1936) - 1.32 + 122$ $\newline$ $P = 11.616 - 1.32 + 122$ $\newline$ $P = 132.296$ $\newline$ Round to the nearest tenth: $P = 132.3$ mmHg.
Solve for y: B.) Solve for y when $P = 130.86$ mmHg. $\newline$ Set the equation $0.006y^2 - 0.03y + 122 = 130.86$ . $\newline$ $0.006y^2 - 0.03y - 8.86 = 0$ $\newline$ Use the quadratic formula $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 0.006$ , $b = -0.03$ , $c = -8.86$ . $\newline$ Discriminant = $(-0.03)^2 - 4 \cdot 0.006 \cdot -8.86$ $\newline$ Discriminant = $0$ . $0009$ + $0$ . $21216$ $\newline$ Discriminant = $0$ . $21306$ $\newline$ $y = \frac{0.03 \pm \sqrt{0.21306}}{0.012}$ $\newline$ $y = \frac{0.03 \pm 0.46158}{0.012}$ $\newline$ $0.006y^2 - 0.03y + 122 = 130.86$ $0$ $\newline$ $0.006y^2 - 0.03y + 122 = 130.86$ $1$ (not possible as age cannot be negative) $\newline$ Round $0.006y^2 - 0.03y + 122 = 130.86$ $2$ to the nearest whole year: $0.006y^2 - 0.03y + 122 = 130.86$ $3$ years.