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: \[ P=0.005 y^{2}-0.02 y+122 \] 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 41 years. \( \square \) B.) If a person's systolic pressure is 130.8 mm Hg , what is their age (rounded to the nearest whole year)? \( \square \)

First, let's solve part A by substituting \( y = 41 \) into the equation \( P = 0.005 y^2 - 0.02 y + 122 \). \[ P = 0.005(41^2) - 0.02(41) + 122 \] \[ P = 0.005(1681) - 0.82 + 122 \] \[ P = 8.405 - 0.82 + 122 \] \[ P = 129.585 \] Rounding it to the nearest tenth, the systolic pressure for a person of age 41 years is **129.6 mm Hg**. Now, for part B, we need to find \( y \) such that \( P = 130.8 \). We set up the equation: \[ 130.8 = 0.005 y^2 - 0.02 y + 122 \] Rearranging: \[ 0.005 y^2 - 0.02 y + 122 - 130.8 = 0 \] \[ 0.005 y^2 - 0.02 y - 8.8 = 0 \] To make calculations easier, multiply the entire equation by 1000: \[ 5y^2 - 20y - 8800 = 0 \] Using the quadratic formula \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \): Here, \( a = 5 \), \( b = -20 \), and \( c = -8800 \). Calculating the discriminant: \[ b^2 - 4ac = (-20)^2 - 4(5)(-8800) \] \[ = 400 + 176000 = 176400 \] Calculating \( y \): \[ y = \frac{-(-20) \pm \sqrt{176400}}{2(5)} \] \[ y = \frac{20 \pm 420}{10} \] Calculating the two potential values for \( y \): \[ y_1 = \frac{440}{10} = 44, \quad y_2 = \frac{-400}{10} = -40 \] Since age cannot be negative, we consider \( y = 44 \). So, if a person’s systolic pressure is 130.8 mm Hg, their age is **44 years**.