Problem

A person's systolic blood pressure, which is measured in millimeters of mercury $(\mathrm{mm} \mathrm{Hg})$, depends on a person's age, in years. The equation:
\[
P=0.004 y^{2}-0.01 y+119
\]
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 46 years.
B.) If a person's systolic pressure is $125.31 \mathrm{~mm} \mathrm{Hg}$, what is their age (rounded to the nearest whole year)?

Answer

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Answer

Final Answer: A.) The systolic pressure for a person of age 46 years is \(\boxed{127.0 \, \mathrm{mmHg}}\). B.) The age of a person whose systolic pressure is $125.31 \, \mathrm{mmHg}$ is \(\boxed{41 \, \mathrm{years}}\).

Steps

Step 1 :Given the equation for systolic blood pressure, \(P=0.004 y^{2}-0.01 y+119\), where \(P\) is the blood pressure in millimeters of mercury and \(y\) is the age in years.

Step 2 :For part A, we substitute \(y=46\) into the equation to find the systolic pressure for a person of age 46 years. This gives us \(P = 0.004 * 46^{2} - 0.01 * 46 + 119\), which simplifies to \(P = 127.004\). Rounding to the nearest tenth of a millimeter, we get \(P = 127.0 \, \mathrm{mmHg}\).

Step 3 :For part B, we substitute \(P=125.31\) into the equation and solve for \(y\). This gives us the quadratic equation \(0.004 y^{2}-0.01 y + 119 - 125.31 = 0\). Solving this equation gives us two possible values for \(y\), -38.49 and 40.99. Since age cannot be negative, we discard the negative value and round the positive value to the nearest whole year, giving us \(y = 41 \, \mathrm{years}\).

Step 4 :Final Answer: A.) The systolic pressure for a person of age 46 years is \(\boxed{127.0 \, \mathrm{mmHg}}\). B.) The age of a person whose systolic pressure is $125.31 \, \mathrm{mmHg}$ is \(\boxed{41 \, \mathrm{years}}\).

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