1. **Problem Statement:** Suresh's factory production changes over 5 years starting from 2003 with the following pattern: - Increase by 12% for two consecutive years - Decrease by 8% in the third year - Repeat the same pattern for the next three years We need to find the overall effect on production by 2007. 2. **Formula and Explanation:** If the initial production is $P_0$, then after an increase of 12%, production becomes $P_1 = P_0 \times (1 + 0.12) = P_0 \times 1.12$. After another 12% increase, $P_2 = P_1 \times 1.12 = P_0 \times 1.12^2$. After an 8% decrease, $P_3 = P_2 \times (1 - 0.08) = P_0 \times 1.12^2 \times 0.92$. 3. **Applying the pattern for 5 years:** The pattern repeats for the next two years: - Year 4: Increase by 12%: $P_4 = P_3 \times 1.12 = P_0 \times 1.12^3 \times 0.92$ - Year 5: Increase by 12%: $P_5 = P_4 \times 1.12 = P_0 \times 1.12^4 \times 0.92$ - Year 6 (2007): Decrease by 8%: $P_6 = P_5 \times 0.92 = P_0 \times 1.12^4 \times 0.92^2$ 4. **Calculate the overall effect:** $$\text{Overall factor} = 1.12^4 \times 0.92^2$$ Calculate each: $1.12^4 = 1.12 \times 1.12 \times 1.12 \times 1.12 = 1.5748$ (approx) $0.92^2 = 0.8464$ Multiply: $$1.5748 \times 0.8464 = 1.333$$ (approx) 5. **Interpretation:** The production in 2007 is approximately $1.333$ times the initial production in 2003, meaning an increase of about 33.3%.