The​ double-bar graph shown displays the average cost of an undergraduate​ student's tuition,​ fees, and room and board for the academic years​ 2012-2013 to​ 2016-2017 at both a​ 2-year and a​ 4-year public institution. What was the percent increase in the average cost at a public 4​-year institution from​ 2012-13 to​ 2016-17?

Question

2012-13
2013-14
2014-15
2015-16
2016-17
0
50
100
150
200
250
300
Academic year
Average Cost (in hundreds of dollars)
4-year
2-year
90
233
95
235
98
239
102
249
108
254

A double-bar graph has a horizontal axis labeled "Academic year" with five labels and a vertical axis labeled "Average Cost (in hundreds of dollars)" from 0 to 300 in increments of 50. Two vertical bars are above each of the horizontal axis labels, where the left bar represents 2-year, and the right bar represents 4-year. The heights of the bars are as follows, where the academic year is listed first, and the heights of the bars are listed next from left to right: 2012-13, 90 and 233; 2013-14, 95 and 235; 2014-15, 98 and 239; 2015-16, 102 and 249; 2016-17, 108 and 254.
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Part 1
The percent increase in the average cost at a 4​-year institution from​ 2012-13 to​ 2016-17 was
  
enter your response here​%.

Answer 1

To calculate the percent increase in the average cost at a public 4-year institution from the academic year 2012-2013 to 2016-2017, we can use the following formula:

\[ \text{Percent Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \]

From the data provided, the average costs for a public 4-year institution were:

• 2012-2013: 233 (in hundreds of dollars)
• 2016-2017: 254 (in hundreds of dollars)

Now, substituting the values into the formula:

1. Old Value (2012-13) = 233
2. New Value (2016-17) = 254

Now calculate the percent increase:

\[ \text{Percent Increase} = \left( \frac{254 - 233}{233} \right) \times 100 \]

\[ = \left( \frac{21}{233} \right) \times 100 \approx 9.01% \]

Thus, the percent increase in the average cost at a public 4-year institution from 2012-13 to 2016-17 was approximately 9.01%.