Questions: In 2014, there were 500 students enrolled in a college course. In 2015, there were 450 students enrolled in this particular course. Select the true statement about students enrolled in this course from 2014 to 2015 (percentages are rounded to the nearest tenths place). a.) The absolute change is 50 students, and the relative change indicates an increase of 11%. b.) The absolute change is 50 students, and the relative change indicates a decrease of 10%. c.) The absolute change is -50 students, and the relative change indicates a decrease of 11%. d.) The absolute change is -50 students, and the relative change indicates a decrease of 10%.

In 2014, there were 500 students enrolled in a college course. In 2015, there were 450 students enrolled in this particular course. Select the true statement about students enrolled in this course from 2014 to 2015 (percentages are rounded to the nearest tenths place). a.) The absolute change is 50 students, and the relative change indicates an increase of 11%. b.) The absolute change is 50 students, and the relative change indicates a decrease of 10%. c.) The absolute change is -50 students, and the relative change indicates a decrease of 11%. d.) The absolute change is -50 students, and the relative change indicates a decrease of 10%.
Transcript text: In 2014, there were 500 students enrolled in a college course. In 2015, there were 450 students enrolled in this particular course. Select the true statement about students enrolled in this course from 2014 to 2015 (percentages are rounded to the nearest tenths place). a.) The absolute change is 50 students, and the relative change indicates an increase of $11 \%$. b.) The absolute change is 50 students, and the relative change indicates a decrease of $10 \%$. c.) The absolute change is -50 students, and the relative change indicates a decrease of $11 \%$. d.) The absolute change is -50 students, and the relative change indicates a decrease of $10 \%$.
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Solution

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Solution Steps

Step 1: Calculate the Absolute Change

The absolute change in the number of students from 2014 to 2015 is calculated by subtracting the number of students in 2015 from the number of students in 2014: \[ \text{Absolute Change} = \text{students}_{2015} - \text{students}_{2014} = 450 - 500 = -50 \]

Step 2: Calculate the Relative Change

The relative change is calculated by dividing the absolute change by the initial number of students (in 2014) and then converting it to a percentage: \[ \text{Relative Change} = \left( \frac{\text{Absolute Change}}{\text{students}_{2014}} \right) \times 100 = \left( \frac{-50}{500} \right) \times 100 = -10.0\% \]

Step 3: Determine the Correct Statement

Based on the calculations:

  • The absolute change is \(-50\) students.
  • The relative change is \(-10.0\%\).

Among the given options, the correct statement is: d.) The absolute change is \(-50\) students, and the relative change indicates a decrease of \(10\%\).

Final Answer

\[ \boxed{\text{d.) The absolute change is -50 students, and the relative change indicates a decrease of 10\%.}} \]

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