To model the decline of the elephant herd, we can use the formula for exponential decay:
\[ y = y_0 \cdot (1 - r)^t \]
where:
- \( y \) is the number of elephants after \( t \) years,
- \( y_0 \) is the initial number of elephants (62 in this case),
- \( r \) is the decay rate (4% or 0.04),
- \( t \) is the time in years.
Given that the herd is declining at a rate of 4% per year, we can express this as:
\[ y = 62 \cdot (1 - 0.04)^t \] \[ y = 62 \cdot (0.96)^t \]
So the correct model for the problem is:
\[ y = 62(0.96)^t \]
The other options you provided do not correctly represent the exponential decay based on a 4% annual decline.
To summarize, the correct exponential decay model is:
Answer: \( y = 62(0.96)^t \)
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