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_=(-\left(b\right)\pm√(\left(b\right)^2-4\cdot\:ac))/(2\cdot\:a) \\ Replacing \\ y_=(-\left(-20\right)\pm√(\left(-20\right)^2-4\cdot\:5\left(-8800\right)))/(2\cdot\:5) \\ y_=(-\left(-20\right)\pm\:420)/(2\cdot\:5) \\ y_1=(-\left(-20\right)+420)/(2\cdot\:5)=44 \\ y_2=(-\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