Question

Question
In a certain geographic location, a herd of elephants is declining at a rate of four percent every year. If there are currently 62 elephants in the herd, create an exponential decay function to model the problem. Let y represent the number of elephants after t years.(1 point)
Responses

y=62(1.04)^t
y equals 62 left parenthesis 1.04 right parenthesis superscript t baseline

y=62(0.6)^t
y equals 62 left parenthesis 0.6 right parenthesis superscript t baseline

y=62(0.96)^t
y equals 62 left parenthesis 0.96 right parenthesis superscript t baseline

y=62(0.04)^t

Answer 1

To model the decline of the elephant herd, we need to use an exponential decay function. The general form of an exponential decay function is:

\[ y = a(1 - r)^t \]

where:
- \( a \) is the initial amount (in this case, the initial number of elephants),
- \( r \) is the decay rate (as a decimal),
- \( t \) is the number of years,
- \( y \) is the amount after \( t \) years.

Given that the herd is declining at a rate of 4 percent per year, we can express this decay rate as \( r = 0.04 \). This means that the proportion of elephants retained each year is \( 1 - r = 1 - 0.04 = 0.96 \).

Thus, the exponential decay function for this scenario becomes:

\[ y = 62(0.96)^t \]

The correct response to the question is:

**y = 62(0.96)^t**