Subjects algebra

Road Length

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Road Length


1. **State the problem:** We are given an initial road length 13 years ago, $L_0 = 1350$ km. 2. For the next 9 years, the road length increased by 29% each year. This means each year the length is multiplied by $1 + 0.29 = 1.29$. After 9 years, the length is: $$L_1 = 1350 \times 1.29^9$$ 3. For the remaining 4 years (since 13 years total - 9 years), the road length increases by 16% each year. Each year, the length is multiplied by $1 + 0.16 = 1.16$. After these 4 years, $$L_2 = L_1 \times 1.16^4 = 1350 \times 1.29^9 \times 1.16^4$$ 4. Calculate values step-by-step: First, $1.29^9 \approx 15.214$ (approximate to 3 decimal places for clarity). Then, $1.16^4 \approx 1.808$. Multiply all: $$L_2 \approx 1350 \times 15.214 \times 1.808 = 1350 \times 27.513 = 37141.1$$ 5. Round to 3 significant figures: $$37100 \text{ km}$$ **Final answer:** The total road length now is approximately $37100$ km to 3 significant figures.