To calculate the number of zebras remaining after a certain number of years, given that they are declining at a rate of 4% each year, you can use the formula for exponential decay:
\[ N = N_0 \times (1 - r)^t \]
Where:
- \( N \) is the number of zebras after \( t \) years.
- \( N_0 \) is the initial number of zebras (72).
- \( r \) is the rate of decline (4%, or 0.04).
- \( t \) is the number of years.
Let's calculate the number of zebras remaining after a specific number of years. Here are a few examples:
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After 1 year: \[ N = 72 \times (1 - 0.04)^1 = 72 \times 0.96 = 69.12 \approx 69 , \text{(rounding down)} \]
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After 2 years: \[ N = 72 \times (1 - 0.04)^2 = 72 \times 0.96^2 = 72 \times 0.9216 \approx 66.24 \approx 66 , \text{(rounding down)} \]
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After 5 years: \[ N = 72 \times (1 - 0.04)^5 = 72 \times 0.96^5 \approx 72 \times 0.8154 \approx 58.747 \approx 58 , \text{(rounding down)} \]
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After 10 years: \[ N = 72 \times (1 - 0.04)^{10} = 72 \times 0.96^{10} \approx 72 \times 0.6648 \approx 47.67 \approx 47 , \text{(rounding down)} \]
You can continue this calculation for any number of years you'd like. Let me know if you want to calculate for a specific number of years!
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