To calculate the number of zebras in the herd each year as it declines at a rate of 4%, you can use the formula for exponential decay:
\[ N(t) = N_0 \times (1 - r)^t \]
Where:
- \(N(t)\) = the number of zebras at time \(t\),
- \(N_0\) = the initial number of zebras (72 in this case),
- \(r\) = the decay rate (4% or 0.04),
- \(t\) = time in years.
Now let's compute the number of zebras for the next few years.
Year 1:
\[ N(1) = 72 \times (1 - 0.04)^1 = 72 \times 0.96 = 69.12 \approx 69 \]
Year 2:
\[ N(2) = 72 \times (1 - 0.04)^2 = 72 \times 0.96^2 = 72 \times 0.9216 \approx 66.23 \approx 66 \]
Year 3:
\[ N(3) = 72 \times (1 - 0.04)^3 = 72 \times 0.96^3 = 72 \times 0.884736 \approx 63.76 \approx 64 \]
Year 4:
\[ N(4) = 72 \times (1 - 0.04)^4 = 72 \times 0.96^4 = 72 \times 0.84934656 \approx 61.00 \approx 61 \]
Year 5:
\[ N(5) = 72 \times (1 - 0.04)^5 = 72 \times 0.96^5 = 72 \times 0.8153726976 \approx 58.70 \approx 59 \]
You can continue this method to find the number of zebras for subsequent years.
If you're interested in a specific year, just let me know, and I can perform that calculation!