Question

A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in yearsThe equation: P = 0.005y ^ 2 - 0.02y + 118 gives a person's blood pressure , P, at age y years

Answer 1

To solve the first part we replace the value of years in the formula in this case 40

$\begin{gathered} P\text{ = 0.005y}^2-0.02y\text{ + 118} \\ P\text{ = 0.005\lparen40\rparen}^2-0.02(40)+118 \\ P\text{ = 8 - 0.8+118 } \\ P=125.2 \end{gathered}$

And for the second part, we replace P = 126.8

$126.8\text{ = 0.005y}^2-0.02y+118$

Reorganizing

$0.005y^2-0.02y-8.8$

And we factorize

$\begin{gathered} y_=\frac{-\left(b\right)\pm\sqrt{\left(b\right)^2-4\cdot\:ac}}{2\cdot\:a} \\ Replacing \\ y_=\frac{-\left(-20\right)\pm\sqrt{\left(-20\right)^2-4\cdot\:5\left(-8800\right)}}{2\cdot\:5} \\ y_=\frac{-\left(-20\right)\pm\:420}{2\cdot\:5} \\ y_1=\frac{-\left(-20\right)+420}{2\cdot\:5}=44 \\ y_2=\frac{-\left(-20\right)-420}{2\cdot\:5}=-40 \end{gathered}$

We get two answers 44 and -44 but the age can not be negative so the answer is 44