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Introductory and Intermediate Algebra for College Students

Your cardiac index is your heart's output, in liters of blood per minute, divided by your body's surface area, in square meters.

The cardiac index, $C(x),$ can be modeled by

\[C(x)=\frac{7.644}{\sqrt[4]{x}}, \quad 10 \leq x \leq 80\]

where $x$ is an individual's age, in years. The graph of the function is shown. Use the function to solve.

a. Find the cardiac index of a 32 -year-old. Express the denominator in simplified radical form and reduce the fraction.

b. Use the form of the answer in part (a) and a calculator to express the cardiac index to the nearest hundredth. Identify your solution as a point on the graph.