Solved on Feb 29, 2024

Find the change in the number of commercial radio stations playing a particular genre of music from 2005 to 2015. The absolute change is $\left| 744 - 398 \right| = 346$ . The relative change is $\left( \frac{398 - 744}{744} \right) \times 100 = -46.5\%$ .

STEP 1

Assumptions
1. The number of commercial radio stations playing a particular genre of music in 2005 is 744.
2. The number of commercial radio stations playing the same genre of music in 2015 is 398.
3. Absolute change is calculated as the difference between the initial and final values.
4. Relative change is calculated as the absolute change divided by the initial value, expressed as a percentage.

STEP 2

Calculate the absolute change by subtracting the number of stations in 2015 from the number of stations in 2005.
$Absolute\, change = Initial\, value - Final\, value$

STEP 3

Plug in the given values for the initial and final number of stations to calculate the absolute change.
$Absolute\, change = 744 - 398$

STEP 4

Calculate the absolute change.
$Absolute\, change = 744 - 398 = 346$

STEP 5

Now, we calculate the relative change by dividing the absolute change by the initial value and then multiplying by 100 to express it as a percentage.
$Relative\, change = \left(\frac{Absolute\, change}{Initial\, value}\right) \times 100\%$

STEP 6

Plug in the values for the absolute change and the initial value to calculate the relative change.
$Relative\, change = \left(\frac{346}{744}\right) \times 100\%$

STEP 7

Calculate the relative change.
$Relative\, change = \left(\frac{346}{744}\right) \times 100\% \approx 46.50537634\%$

STEP 8

Round the relative change to the nearest tenth as needed.
$Relative\, change \approx 46.5\%$
The absolute change is 346. The relative change is 46.5%.

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Find the change in the number of commercial radio stations playing a particular genre of music from 2005 to 2015. The absolute change is $\left| 744 - 398 \right| = 346$ . The relative change is $\left( \frac{398 - 744}{744} \right) \times 100 = -46.5\%$ .

STEP 1

STEP 2

Calculate the absolute change by subtracting the number of stations in 2015 from the number of stations in 2005.
$Absolute\, change = Initial\, value - Final\, value$

STEP 3

Plug in the given values for the initial and final number of stations to calculate the absolute change.
$Absolute\, change = 744 - 398$

STEP 4

Calculate the absolute change.
$Absolute\, change = 744 - 398 = 346$

STEP 5

Now, we calculate the relative change by dividing the absolute change by the initial value and then multiplying by 100 to express it as a percentage.
$Relative\, change = \left(\frac{Absolute\, change}{Initial\, value}\right) \times 100\%$

STEP 6

Plug in the values for the absolute change and the initial value to calculate the relative change.
$Relative\, change = \left(\frac{346}{744}\right) \times 100\%$

STEP 7

Calculate the relative change.
$Relative\, change = \left(\frac{346}{744}\right) \times 100\% \approx 46.50537634\%$

STEP 8

Round the relative change to the nearest tenth as needed.
$Relative\, change \approx 46.5\%$
The absolute change is 346. The relative change is 46.5%.

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STEP 1

STEP 2

Calculate the absolute change by subtracting the number of stations in 2015 from the number of stations in 2005.Absolute change=Initial value−Final valueAbsolute\, change = Initial\, value - Final\, valueAbsolutechange=Initialvalue−Finalvalue

STEP 3

Plug in the given values for the initial and final number of stations to calculate the absolute change.Absolute change=744−398Absolute\, change = 744 - 398Absolutechange=744−398

STEP 4

Calculate the absolute change.Absolute change=744−398=346Absolute\, change = 744 - 398 = 346Absolutechange=744−398=346

STEP 5

STEP 6

Plug in the values for the absolute change and the initial value to calculate the relative change.Relative change=(346744)×100%Relative\, change = \left(\frac{346}{744}\right) \times 100\%Relativechange=(744346​)×100%

STEP 7

Calculate the relative change.Relative change=(346744)×100%≈46.50537634%Relative\, change = \left(\frac{346}{744}\right) \times 100\% \approx 46.50537634\%Relativechange=(744346​)×100%≈46.50537634%

STEP 8

Round the relative change to the nearest tenth as needed.Relative change≈46.5%Relative\, change \approx 46.5\%Relativechange≈46.5%The absolute change is 346. The relative change is 46.5%.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Calculate the absolute change by subtracting the number of stations in 2015 from the number of stations in 2005.
$Absolute\, change = Initial\, value - Final\, value$

Plug in the given values for the initial and final number of stations to calculate the absolute change.
$Absolute\, change = 744 - 398$

Calculate the absolute change.
$Absolute\, change = 744 - 398 = 346$

Plug in the values for the absolute change and the initial value to calculate the relative change.
$Relative\, change = \left(\frac{346}{744}\right) \times 100\%$

Calculate the relative change.
$Relative\, change = \left(\frac{346}{744}\right) \times 100\% \approx 46.50537634\%$

Round the relative change to the nearest tenth as needed.
$Relative\, change \approx 46.5\%$
The absolute change is 346. The relative change is 46.5%.