Questions: Calculate absolute change and relative change. In 2015, there were 210 participants in a trivia competition, In 2016, there were 298 participants in this trivia competition. Select the true statement about participants in the trivia competition from 2015 to 2016. Percentages are rounded to the nearest tenths place. a.) The absolute change is 88 participants and the relative change indicates an increase of 42%. b.) The absolute change is 88 participants and the relative change indicates an increase of 0.42%. C) The absolute change is -88 participants and the relative change indicates a decrease of 42%. d) The absolute change is -88 participants and the relative change indicates a decrease of 0.42%.

Calculate absolute change and relative change. In 2015, there were 210 participants in a trivia competition, In 2016, there were 298 participants in this trivia competition. Select the true statement about participants in the trivia competition from 2015 to 2016. Percentages are rounded to the nearest tenths place. a.) The absolute change is 88 participants and the relative change indicates an increase of 42%. b.) The absolute change is 88 participants and the relative change indicates an increase of 0.42%. C) The absolute change is -88 participants and the relative change indicates a decrease of 42%. d) The absolute change is -88 participants and the relative change indicates a decrease of 0.42%.
Transcript text: Calculate absolute change and relative change. In 2015, there were 210 participants in a trivia competition, In 2016, there were 298 participants in this trivia competition. Select the true statement about participants in the trivia competition from 2015 to 2016. Percentages are rounded to the nearest tenths place. a.) The absolute change is 88 participants and the relative change indicates an increase of $42 \%$. b.) The absolute change is 88 participants and the relative change indicates an increase of $0.42 \%$. C) The absolute change is - 88 participants and the relative change indicates a decrease of $42 \%$. d) The absolute change is -88 participants and the relative change indicates a decrease of $0.42 \%$.
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Solution

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Solution Steps

To solve this problem, we need to calculate both the absolute change and the relative change in the number of participants from 2015 to 2016. The absolute change is simply the difference in the number of participants between the two years. The relative change is the absolute change divided by the initial value (number of participants in 2015), expressed as a percentage.

Step 1: Calculate Absolute Change

The absolute change in the number of participants from 2015 to 2016 is given by: \[ \text{Absolute Change} = \text{Participants}_{2016} - \text{Participants}_{2015} = 298 - 210 = 88 \]

Step 2: Calculate Relative Change

The relative change is calculated using the formula: \[ \text{Relative Change} = \left( \frac{\text{Absolute Change}}{\text{Participants}_{2015}} \right) \times 100 = \left( \frac{88}{210} \right) \times 100 \approx 41.9 \]

Step 3: Analyze the Options

Based on the calculations:

  • The absolute change is \( 88 \) participants.
  • The relative change is approximately \( 41.9\% \).

Now, we can evaluate the provided options:

  • a.) The absolute change is \( 88 \) participants and the relative change indicates an increase of \( 41\% \). (True)
  • b.) The absolute change is \( 88 \) participants and the relative change indicates an increase of \( 0.42\% \). (False)
  • c.) The absolute change is \( -88 \) participants and the relative change indicates a decrease of \( 42\% \). (False)
  • d.) The absolute change is \( -88 \) participants and the relative change indicates a decrease of \( 0.42\% \). (False)

Final Answer

The correct statement is option A. Thus, the answer is: \[ \boxed{A} \]

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