Question

A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equation:

P=0.005y^2−0.01y+121

gives a person's 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.



B.) If a person's systolic pressure is 133 mm Hg, what is their age (rounded to the nearest whole year)?

Answer 1

a) 132.0 mmHg, b) 50 years old.

Explanation:

a) Plug in 48 where you see the letter y and simplify, preferably with a calculator.

P = 0.005(48)^2 - 0.01(48) + 121

P = 132.04 mmHg, to the nearest tenth would be 132.0 mmHg

b) Plug in 133 for P and solve for y.

0.005y^2 - 0.01 + 121 = 133

To make it a little easier on myself -- and because I haven't practiced a diff. method in a while -- I simplified the equation to 0.005y^2 - 0.01y - 12 = 0 by subtracting 133 from both sides. I did that so that I can could then use the quadratic formula to solve.

Quadratic formula is y = (-b +/- √(b^2 - 4ac)) / 2

Now we plug in our given information, that new trinomial, to solve for y

`y = (0.01 +/- √((0.01)^2 - 4(0.005)(-12)) )/(2(.0.005)) \\y = (0.01 +/- √(0.2401))/(0.01)`

`y = (0.01)/(0.01) +/- (√(0.2401))/(0.01) \\y = 1 +/- (0.49)/(0.01)\\y = 1+/- 49`

Because it is a trinomial, you are given two answers. You get y = 48 and y = 50. In order to find out which is right, you plug in and see which on yields 133 as the answer. Given the part a), I already know it's not 48. When I plug in 50, I get 133. Therefore, 50 years old is your answer.