A person's systolic blood pressure, which is measured in millimeters of mercury (mmHg), depends on a person's age, in years. The equation: P=0.006y^(2)-0.03 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 44 years. B.) If a person's systolic pressure is 130.86mmHg, what is their age (rounded to the nearest whole year)?

Question

A person's systolic blood pressure, which is measured in millimeters of mercury  (mmHg), depends on a person's age, in years. The equation:  P=0.006y^(2)-0.03 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 44 years. B.) If a person's systolic pressure is  130.86mmHg, what is their age (rounded to the nearest whole year)?

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Calculate Systolic Pressure:  A.) Calculate the systolic pressure for a person aged 44 years. Substitute y = 44 into the equation P = 0.006y^2 - 0.03y + 122. P = 0.006(44)^2 - 0.03(44) + 122 P = 0.006(1936) - 1.32 + 122 P = 11.616 - 1.32 + 122 P = 132.296 Round to the nearest tenth: P = 132.3 mmHg.Solve for y:  B.) Solve for y when P = 130.86 mmHg. Set the equation 0.006y^2 - 0.03y + 122 = 130.86. 0.006y^2 - 0.03y - 8.86 = 0 Use the quadratic formula y = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = 0.006, b = -0.03, c = -8.86. Discriminant = (-0.03)^2 - 4 * 0.006 * -8.86 Discriminant = 0.0009 + 0.21216 Discriminant = 0.21306 y = (0.03 ± sqrt(0.21306)) / 0.012 y = (0.03 ± 0.46158) / 0.012 y1 = (0.03 + 0.46158) / 0.012 = 40.965 y2 = (0.03 - 0.46158) / 0.012 = -36.0483 (not possible as age cannot be negative) Round y1 to the nearest whole year: y = 41 years.

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