Understanding the College Admissions Data

The provided table shows the number of students admitted to three different colleges (A, B, and C) over six years, from 2014 to 2019. Each row represents a year, and each column represents a college, showing the number of students admitted in that specific college during that specific year.

We are asked to find the approximate percent increase in the number of students admitted in college A in the year 2016 as compared to the previous year, which is 2015.

Identifying the Relevant Data for College A

To find the percent increase in college A admissions from 2015 to 2016, we need the number of students admitted in college A for both these years:

• Number of students admitted in College A in 2015 (Previous Year)
• Number of students admitted in College A in 2016 (Current Year)

Looking at the table:

• Students admitted in College A in 2015 = 15000
• Students admitted in College A in 2016 = 17000

Calculating the Percent Increase

The formula for calculating the percent increase is:

\(\text{Percent Increase} = \frac{(\text{Current Value} - \text{Original Value})}{\text{Original Value}} \times 100\%\)

In this case:

• Original Value = Number of students in College A in 2015 = 15000
• Current Value = Number of students in College A in 2016 = 17000

First, calculate the increase in the number of students:

\(\text{Increase} = \text{Students in 2016} - \text{Students in 2015}\)

\(\text{Increase} = 17000 - 15000\)

\(\text{Increase} = 2000\)

Now, calculate the percent increase:

\(\text{Percent Increase} = \frac{\text{Increase}}{\text{Students in 2015}} \times 100\%\)

\(\text{Percent Increase} = \frac{2000}{15000} \times 100\%\)

Simplify the fraction:

\(\text{Percent Increase} = \frac{2}{15} \times 100\%\)

\(\text{Percent Increase} = \frac{200}{15}\%\)

\(\text{Percent Increase} = \frac{40}{3}\%\)

Now, convert the fraction to a decimal:

\(\frac{40}{3} \approx 13.33...\%\)

Approximating the Result

The question asks for the approximate percent increase. Rounding 13.33...% to the nearest whole number gives 13%.

Thus, the approximate percent increase in the number of students admitted in college A in the year 2016 as compared to the previous year is 13%.

Revision Table: College A Admissions 2015-2016

Here's a summary of the values used for the calculation:

Additional Information: Understanding Percentage Change

Percentage change is a way to express how much a quantity changes relative to its original value. It is commonly used in various fields, including finance, statistics, and economics, to understand growth or decline.

• Percent Increase: Occurs when the new value is greater than the original value. Calculated as \(\frac{(\text{New - Original})}{\text{Original}} \times 100\%\).
• Percent Decrease: Occurs when the new value is less than the original value. Calculated as \(\frac{(\text{Original - New})}{\text{Original}} \times 100\%\) or as the absolute value of \(\frac{(\text{New - Original})}{\text{Original}} \times 100\%\).
• Base Value: When calculating percent change, the 'original value' or 'previous year's value' serves as the base for the calculation. This is crucial as changing the base changes the percentage.

In this problem, the base value is the number of students in 2015, as we are comparing 2016 admissions as compared to the previous year (2015).