Question

A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as P = 0.006A*2-0.02A + 120. Find the age of a man whose normal blood pressure measures 129 mmHg. Round your answer to the nearest year. The man would be ? years old.​

Answer 1

The man would be 40 years old.

Explanation:

Blood pressure as function of age:

Is given by the following equation:

`P = 0.006A^2 - 0.02A + 120`

Find the age of a man whose normal blood pressure measures 129 mmHg.

This is A for which P = 129. So

`129 = 0.006A^2 - 0.02A + 120`

`0.006A^2 - 0.02A - 9 = 0`

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\Delta))/(2*a)`

`x_(2) = (-b - √(\Delta))/(2*a)`

`\Delta = b^(2) - 4ac`

In this question:

Quadratic equation with
`a = 0.006, b = -0.02, C = -9`. So

`\Delta = (-0.02)^2 - 4(0.006)(-9) = 0.2164`

`A_(1) = (-(-0.02) + √(0.2164))/(2*(0.006)) = 40.4`

`A_(2) = (-(-0.02) - √(0.2164))/(2*(0.006)) = -37.1`

Age has to be a positive number, so rounding to the nearest year:

The man would be 40 years old.