Question

score: 6/30 answered: 1/4
question 2
a persons systolic blood pressure, which is measured in millimeters of mercury (mm hg), depends on a persons age, in years. the equation: $p(y)=0.005y^{2}-0.02y + 119$ gives a persons blood pressure, $p$, at age $y$ years.
a.) find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 48 years.
mm hg
b.) if a persons systolic pressure is 127.8 mm hg, what is their age (rounded to the nearest whole year)?
years old
question help: message instructor

Explanation:

Step1: Substitute age into formula for part A

Substitute $y = 48$ into $P(y)=0.005y^{2}-0.02y + 119$.
$P(48)=0.005\times(48)^{2}-0.02\times48 + 119$

Step2: Calculate each term for part A

First term: $0.005\times(48)^{2}=0.005\times2304 = 11.52$.
Second term: $0.02\times48 = 0.96$.
Then $P(48)=11.52-0.96 + 119$.
$P(48)=129.56\approx129.6$ mm Hg.

Step3: Set up equation for part B

Set $P(y)=127.8$, so $0.005y^{2}-0.02y + 119 = 127.8$.
Rearrange to get $0.005y^{2}-0.02y-8.8 = 0$.
Multiply through by 1000 to clear decimals: $5y^{2}-20y - 8800=0$.
Divide by 5: $y^{2}-4y - 1760=0$.

Step4: Solve quadratic equation for part B

Use the quadratic formula $y=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ for $ay^{2}+by + c = 0$. Here $a = 1$, $b=-4$, $c=-1760$.
First calculate the discriminant $\Delta=b^{2}-4ac=(-4)^{2}-4\times1\times(-1760)=16 + 7040=7056$.
Then $y=\frac{4\pm\sqrt{7056}}{2}=\frac{4\pm84}{2}$.
We have two solutions: $y_1=\frac{4 + 84}{2}=44$ and $y_2=\frac{4-84}{2}=-40$. Since age cannot be negative, the age is 44 years.

Answer:

A. 129.6 mm Hg
B. 44 years old