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. %

Solution Steps

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 \(59.1818\).

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.

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