To create an exponential decay function to model the population of elephants declining at a rate of 4% per year, we can start with the initial number of elephants, which is 62.
Since the herd is declining at a rate of 4%, the remaining population after one year will be 96% of the current population. This is calculated as follows:
1 - decay rate = 1 - 0.04 = 0.96.
The exponential decay function can be expressed as:
\[ y = y_0 \cdot (1 - r)^t \]
where:
- \( y_0 \) is the initial amount (62 elephants),
- \( r \) is the decay rate (0.04), and
- \( t \) is the number of time periods (years).
Substituting in our values, we get:
\[ y = 62 \cdot (0.96)^t \]
So the correct response is:
y = 62(0.96)^t
y equals 62 left parenthesis 0.96 right parenthesis superscript t baseline.
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