Math Problem Statement
Complete parts (a) through (d) below for the time period shown in the accompanying figures.
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Part 1
a. In what academic year did public college tuition rise by the largest percentage, and about what was that percentage?
Public college tuition rose by the largest percentage in
▼ 2003-04
2011-12
2001-02
2016-17
by about
▼ 8%.
15%.
5%.
13%.
Part 2
b. In the year found in part (a), about what was the percentage increase in private college tuition?
The percentage increase in private college tuition was about
▼ 8%
5%
2%
12%
in that year.
Part 3
c. In the year found in part (a), which had the larger increase in actual tuition (in dollars), public or private colleges? Explain. Choose the correct answer below.
A.
Private college tuition rose more in terms of dollars. Since their tuition was so much higher than public colleges, a lower percentage increase on private college tuition can be larger than a higher percentage increase on public college tuition.
B.
Private college tuition rose more in terms of dollars since their percentage increase was higher than the percentage increase of public college tuition.
C.
Public college tuition rose more in terms of dollars. Since their tuition was so much higher than private colleges, a lower percentage increase on public college tuition can be larger than a higher percentage increase on private college tuition.
D.
Public college tuition rose more in terms of dollars since their percentage increase was higher than the percentage increase of private college tuition.
Part 4
d. Overall, does the general trend in percentage change for public and private schools appear to be downward or upward? What about the general trend in actual tuition?
The general trend in percentage change for public and private schools appears to be
▼ downward
upward
and the general trend in actual tuition appears to be
▼ upward.
downward.
Solution
Let's address each part of the question using the provided graphs.
Part 1 (a): Public College Tuition Largest Percentage Increase
Looking at Figure 1, which shows the percentage change in tuition, the largest increase in public college tuition occurred in the academic year 2003-04, where the percentage was the highest. The rise appears to be about 13% in that year.
Answer:
Public college tuition rose the most in 2003-04 by about 13%.
Part 2 (b): Percentage Increase in Private College Tuition in the Same Year
In the academic year 2003-04, private college tuition increased by a lower percentage compared to public colleges. From Figure 1, the private college tuition increase was about 6%.
Answer:
The percentage increase in private college tuition in 2003-04 was about 6%.
Part 3 (c): Larger Dollar Increase in 2003-04: Public vs. Private Colleges
Since private college tuition starts at a much higher base, even a smaller percentage increase can result in a higher dollar increase compared to public colleges. Although public colleges had a larger percentage increase (13%), private colleges had a larger absolute dollar increase.
Answer:
The correct answer is A:
Private college tuition rose more in terms of dollars. Since their tuition was higher than public colleges, a lower percentage increase on private college tuition can be larger than a higher percentage increase on public college tuition.
Part 4 (d): General Trends in Percentage Change and Actual Tuition
From Figure 1, the percentage change in tuition for both public and private colleges shows a downward trend over time after peaking in the early 2000s.
From Figure 2, however, the actual tuition for both public and private colleges shows an upward trend continuously across the years.
Answer:
The general trend in percentage change for public and private schools is downward, and the general trend in actual tuition is upward.
Would you like to explore these details further or ask for clarification? Here are five related questions to expand on this:
- How do percentage changes in tuition affect student debt levels?
- What factors could have caused the spike in public tuition around 2003-04?
- How do public and private colleges differ in terms of initial tuition costs?
- Are there any trends in tuition reduction, or does it increase continuously?
- How does inflation correlate with the tuition increases shown?
Tip: Always consider both the percentage increase and the initial cost when comparing price changes over time—higher initial values can lead to larger absolute increases even with lower percentages.
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Math Problem Analysis
Mathematical Concepts
Percentage Change
Comparing Increases
Trend Analysis
Formulas
Percentage Change = (New Value - Old Value) / Old Value * 100
Theorems
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Suitable Grade Level
Grades 10-12