The bar graph shows the average cost of tuition and fees at private four-year colleges in the United States. Source: The College Board The formula T = 21 x 2 + 862 x + 15 , 552 models the average cost of tuition and fees, T, at private U.S. colleges for the school year ending x years after 2000. Use this information to solve Exercises 131–132. 131. a. Use the formula to find the average cost of tuition and fees at private U.S. colleges for the school year ending in 2014. b. By how much does the formula underestimate or overestimate the actual cost shown by the graph for the school year ending in 2014? c. Use the formula to project the average cost of tuition and fees at private U.S. colleges for the school year ending in 2020.
The bar graph shows the average cost of tuition and fees at private four-year colleges in the United States. Source: The College Board The formula T = 21 x 2 + 862 x + 15 , 552 models the average cost of tuition and fees, T, at private U.S. colleges for the school year ending x years after 2000. Use this information to solve Exercises 131–132. 131. a. Use the formula to find the average cost of tuition and fees at private U.S. colleges for the school year ending in 2014. b. By how much does the formula underestimate or overestimate the actual cost shown by the graph for the school year ending in 2014? c. Use the formula to project the average cost of tuition and fees at private U.S. colleges for the school year ending in 2020.
Solution Summary: The author calculates the average cost of tuition and fees at U.S. colleges for the school year ending in 2014, which is 31,736.
The bar graph shows the average cost of tuition and fees at private four-year colleges in the United States.
Source: The College Board
The formula
T
=
21
x
2
+
862
x
+
15
,
552
models the average cost of tuition and fees, T, at private U.S. colleges for the school year ending x years after 2000. Use this information to solve Exercises 131–132.
131. a. Use the formula to find the average cost of tuition and fees at private U.S. colleges for the school year ending in 2014.
b. By how much does the formula underestimate or overestimate the actual cost shown by the graph for the school year ending in 2014?
c. Use the formula to project the average cost of tuition and fees at private U.S. colleges for the school year ending in 2020.
Solve the variation problems in Exercises 68–73.
68. A company's profit varies directly as the number of products
it sells. The company makes a profit of $1175 on the sale
of 25 products. What is the company's profit when it sells
105 products?
69. The distance that a body falls from rest varies directly as
the square of the time of the fall. If skydivers fall 144 feet in
3 seconds, how far will they fall in 10 seconds?
70. The pitch of a musical tone varies inversely as its wavelength.
A tone has a pitch of 660 vibrations per second and a
wavelength of 1.6 feet. What is the pitch of a tone that has a
wavelength of 2.4 feet?
71. The loudness of a stereo speaker, measured in decibels, varies
inversely as the square of your distance from the speaker.
When you are 8 feet from the speaker, the loudness is
28 decibels. What is the loudness when you are 4 feet from the
speaker?
72. The time required to assemble computers varies directly as the
number of computers assembled and inversely as…
b) Tuition and fees T during year x at private
colleges can be modeled by T = 755.7(x-
1985) + 6121.
According to the model, what was the tuition
and fees in 2014?
Write your answer in a complete sentence.
Use the fact that 14 gallons is approximately the same amount as 53 liters to find a mathematical model that relates liters y to gallons x.Then use the model to find the numbers of liters in 5 gallons and 25 gallons.
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