Questions: The revenue of a certain company decreased by 8% in the first quarter, decreased by 14% in the second quarter, decreased by 15% in the third quarter, and decreased by 12% in the fourth quarter. Did revenue increase or decrease overall? It increased It decreased What is the average rate of growth or decline? Enter your answer as a positive number in percent form, rounded to one decimal places. %

The revenue of a certain company decreased by 8% in the first quarter, decreased by 14% in the second quarter, decreased by 15% in the third quarter, and decreased by 12% in the fourth quarter. Did revenue increase or decrease overall? It increased It decreased What is the average rate of growth or decline? Enter your answer as a positive number in percent form, rounded to one decimal places. %
Transcript text: The revenue of a certain company decreased by $8 \%$ in the first quarter, decreased by $14 \%$ in the second quarter, decreased by $15 \%$ in the third quarter, and decreased by $12 \%$ in the fourth quarter. Did revenue increase or decrease ovgrall? It increased It decreased What is the average rate of growth or decline? Enter your answer as a positive number in percent form, rounded to one decimal places. $\square$ $\%$
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Solution

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Solution Steps

Step 1: Calculate the Final Revenue

The initial revenue is set to \(100\). We apply the percentage changes sequentially for each quarter:

  1. First quarter: Decrease by \(8\%\) \[ 100 \times (1 - 0.08) = 92 \]

  2. Second quarter: Decrease by \(14\%\) \[ 92 \times (1 - 0.14) = 79.12 \]

  3. Third quarter: Decrease by \(15\%\) \[ 79.12 \times (1 - 0.15) = 67.252 \]

  4. Fourth quarter: Decrease by \(12\%\) \[ 67.252 \times (1 - 0.12) = 59.18176 \]

The final revenue after all four quarters is approximately \(59.1818\).

Step 2: Calculate the Overall Percentage Change

The overall percentage change in revenue is calculated as follows: \[ \text{Overall Change} = \left(\frac{59.18176 - 100}{100}\right) \times 100 = -40.81824\% \]

This indicates a decrease in revenue.

Step 3: Calculate the Average Rate of Change

The average rate of change per quarter is the total percentage change divided by the number of quarters: \[ \text{Average Rate of Change} = \frac{-40.81824}{4} = -10.20456\% \]

The average rate of decline per quarter is approximately \(10.20\%\).

Final Answer

The revenue decreased overall, and the average rate of decline per quarter is \(\boxed{10.2\%}\).

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