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 ) = 7.644 x 4 , 10 ≤ x ≤ 80 , where x is an individual’s age, in years. The graph of the function is shown. Use the function to solve Exercises 95–96. 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.
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 ) = 7.644 x 4 , 10 ≤ x ≤ 80 , where x is an individual’s age, in years. The graph of the function is shown. Use the function to solve Exercises 95–96. 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.
Solution Summary: The author explains how to calculate the cardiac index of a 32-year-old to the nearest hundredth.
Yourcardiac indexis 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
)
=
7.644
x
4
,
10
≤
x
≤
80
,
where
x
is an individual’s age, in years. The graph of the function is shown. Use the function to solve Exercises 95–96.
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.
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
7.644
C(x) =
10 s xs 80,
where x is an individual's age, in years. The graph of the function
is shown. Use the function to solve Exercises 95–96.
7.644
C(x) =
%3D
10 20 30 40 50 60 70 80 90
Age
95. 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.
96. a. Find the cardiac index of an 80-year-old. Express the
denominator in simplified radical form and reduce the
fraction.
Cardiac Index
liters per minute
squar e met ers
654 32
In Exercises 7–12, describe the relationship between the two quantities.
America is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected increase in the number of Americans ages 65–84, in millions, from 2030 to 2060. Express this difference in simplified radicalform.b. Use a calculator and write your answer in part (a) to the nearest tenth. Does this rounded decimal overestimate or underestimate the difference in the projected data shown by the bar graph ? By how much?
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