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Applications of Radical Functions
Some situations can be modeled using radical functions. A radical
function is a function that can be described by a radical expression.
1. A basketball player’s hang time is the time spent in the air when shooting a
d
basket. The formula t =
models hang time, t, in seconds, in terms of the
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vertical distance of a player’s jump, d, in feet. When a particular player
dunked a basketball, his hang time for the shot was approximately 1.29
seconds. What was the vertical distance, d, of his jump, rounded to the
nearest tenth?
2. The formula J = 2.7 x + 34 models the percentage of full-time college
students with jobs x years after 1980. Use the formula to project when 63.7%
of full-time college students will have jobs.
3. For each planet in the solar system, its year is the time it takes the planet to
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revolve around the center star. The formula E = 0.2 x 2 models the number of
Earth days in a planet’s year, E, where x is the average distance of the planet
from the center star, in millions of kilometers. There are approximately 365
Earth days in the year of Planet C. What is the average distance of Planet C
from the center star?
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4. The function f(x) = 27 x models the number of plant species, f(x), on an
island in terms of the area, x, in square miles. What is the area of an island
that has 105 species of plants?
5. In psychology, it has been suggested that the number S of nonsense syllables
that a person can repeat consecutively depends on his or her IQ score I
according to the equation S = 2 I – 9. Use this relationship to estimate the
IQ of a person who can repeat 10 nonsense syllables consecutively.
L
can be used to find the period T, in seconds, of a
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pendulum of length L, in feet. What is the length of a pendulum that has a
period of 2.2 seconds? Use 3.14 for  .
6. The formula T = 2 
7. The maximum distance D(h) in kilometers that a person can see from a height
h kilometers above the ground is given by the function D(h) = 111.7 h . Find
the height that would allow a person to see 25 kilometers.
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L
can be used to find the period T, in seconds, of a
9 .8
pendulum of length L, in meters. Find the length of a pendulum that has a
period of 3  seconds.
8. The formula T = 2 
h
can be used to find the distance, h,
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in feet, that the object has fallen after a time, t, in seconds. How far has the
object fallen after 1.6 seconds?
9. For a dropped object, the formula t =
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2D can be used to approximate the speed S, in miles
2
per hour, of a car that has left skid marks of length D, in feet. How far will a
car skid at 50 mph?
10. The formula S =
11. If a penny is dropped off a building, the time it takes (seconds) to fall d feet is
d
given by t =
. If a penny is dropped off a 1280-foot-tall building, how
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long will it take until it hits the ground? Round to the nearest second.
12. If a ball is dropped off a building, the time it takes (seconds) to fall d meters
d
is approximately given by t =
. If a ball is dropped off a 600-meter-tall
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building, how long will it take until it hits the ground? Round to the nearest
second.
13. Kepler’s Law: The square of the period p (years) of a planet’s orbit around
the sun is equal to the cube of the planet’s maximum distance from the sun,
d (in astronomical units or AU). This relationship can be expressed
mathematically as p2 = d3. If this formula is solved for d, the resulting
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equation is d  p 3 . If Saturn has an orbital period of 29.46 Earth years,
calculate Saturn’s maximum distance from the sun to the nearest hundredth
of an AU.
14. The period (in seconds) of a pendulum of length L (meters) is given
L
by P  2
. If a certain pendulum has a length of 19.6 meters,
9.8
determine the period of this pendulum to the nearest tenth of a second.
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1. The jump was 6.7 feet.
2. In 2101, 63.7% of full-time college students will have jobs.
3. The average distance is approximately 149 million kilometers.
4. 58.8 square miles
5. I = 90
6. The length of a pendulum that has a period of 2.2 seconds is 3.93 feet.
7. h = 0.05 km
8. The length of a pendulum that has a period of 3  seconds is 22.05 meters.
9. The object has fallen 40.96 feet in 1.6 seconds.
10. The car will skid 102.04 feet.
11. 9 seconds
12. 11 seconds
13. 9.54 AU
14. 8.9 seconds
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