Subjects exponential decay

Forestland Decay C448C2

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1. **State the problem:** The forestland is decreasing by 2% per year. We start with 4,500,000 acres and want to find the amount after 5 years. 2. **Formula used:** For exponential decay, the amount after $t$ years is given by: $$ A = A_0 (1 - r)^t $$ where $A_0$ is the initial amount, $r$ is the decay rate (as a decimal), and $t$ is the time in years. 3. **Identify values:** - Initial amount $A_0 = 4,500,000$ - Decay rate $r = 0.02$ - Time $t = 5$ 4. **Calculate:** $$ A = 4,500,000 \times (1 - 0.02)^5 = 4,500,000 \times 0.98^5 $$ 5. **Evaluate $0.98^5$:** $$ 0.98^5 = 0.9039207968 $$ 6. **Multiply:** $$ A = 4,500,000 \times 0.9039207968 = 4,067,643.5856 $$ 7. **Round to nearest whole number:** $$ A \approx 4,067,644 $$ **Final answer:** After 5 years, there will be approximately 4,067,644 acres of forestland remaining.