Soru:
A city's annual waste production, \(W\), in tons, is modeled by the equation \(W = 50,000 + 1000p\), where \(p\) is the population in thousands. If the city launches a successful recycling program that reduces waste by \(20\%\), what is the new equation for the annual waste production?
Çözüm:
💡 We need to apply a 20% reduction to the entire original waste equation.
- ➡️ Step 1: Understand the original model. The annual waste is \(W = 50,000 + 1000p\).
- ➡️ Step 2: A 20% reduction means the city keeps 80% of its original waste. (Because 100% - 20% = 80%).
- ➡️ Step 3: To find the new waste amount, we multiply the entire original equation by \(0.80\) (which is 80%).
- ➡️ Step 4: Perform the multiplication:
New Waste = \(0.80 \times (50,000 + 1000p)\)
New Waste = \(0.80 \times 50,000 + 0.80 \times 1000p\)
New Waste = \(40,000 + 800p\)
✅ The new equation for the annual waste production is \(W_{\text{new}} = 40,000 + 800p\).
