The revenue of a certain company decreased by \( 15 \% \) in the first quarter, decreased by \( 15 \% \) in the second quarter, increased by \( 10 \% \) in the third quarter, and decreased by \( 8 \% \) 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.
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To determine whether the revenue increased or decreased overall, we can calculate the revenue at the end of each quarter, assuming an initial revenue of \( R \). 1. After a 15% decrease in the first quarter: \( R_1 = R \times (1 - 0.15) = R \times 0.85 \) 2. After another 15% decrease in the second quarter: \( R_2 = R_1 \times (1 - 0.15) = R \times 0.85 \times 0.85 = R \times 0.7225 \) 3. After a 10% increase in the third quarter: \( R_3 = R_2 \times (1 + 0.10) = R \times 0.7225 \times 1.10 = R \times 0.79475 \) 4. After an 8% decrease in the fourth quarter: \( R_4 = R_3 \times (1 - 0.08) = R \times 0.79475 \times 0.92 = R \times 0.73195 \) Now, we can see the final revenue: \( R_4 = R \times 0.73195 \) This indicates that the revenue decreased overall from the original amount. To find the average rate of growth or decline, we can use the formula for the overall percentage change: Percentage Change = \(\frac{R_{\text{final}} - R_{\text{initial}}}{R_{\text{initial}}} \times 100\) Substituting the values gives us: Percentage Change = \(\frac{0.73195R - R}{R} \times 100 = (0.73195 - 1) \times 100 = -26.805\) So, the revenue decreased by approximately \( 26.8\% \). In conclusion, the answer is: It decreased Average rate of decline: \( 26.8\% \)
