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

Answer:

The man would be 40 years old.

Step-by-step 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:

$ax^{2} + bx + c, a\neq0$.

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:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

In this question:

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

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

$A_{1} = \frac{-(-0.02) + \sqrt{0.2164}}{2*(0.006)} = 40.4$

$A_{2} = \frac{-(-0.02) - \sqrt{0.2164}}{2*(0.006)} = -37.1$

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

The man would be 40 years old.