Question

Zebras are declining at a rate of 4% each year The herd currently has 72

Answer 1

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:

1. **After 1 year:**
\[
N = 72 \times (1 - 0.04)^1 = 72 \times 0.96 = 69.12 \approx 69 \, \text{(rounding down)}
\]

2. **After 2 years:**
\[
N = 72 \times (1 - 0.04)^2 = 72 \times 0.96^2 = 72 \times 0.9216 \approx 66.24 \approx 66 \, \text{(rounding down)}
\]

3. **After 5 years:**
\[
N = 72 \times (1 - 0.04)^5 = 72 \times 0.96^5 \approx 72 \times 0.8154 \approx 58.747 \approx 58 \, \text{(rounding down)}
\]

4. **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!