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

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

y=62(0.04)t
y equals 62 left parenthesis 0.04 right parenthesis superscript t baseline

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

Answer 1

To model the decline of the elephant herd with an exponential decay function, we start with the initial population of elephants, which is 62. The herd is decreasing at a rate of 4% per year.

To express this situation mathematically, we can use the formula for exponential decay:

\[
y = y_0 (1 - r)^t
\]

where:
- \( y \) is the population after \( t \) years,
- \( y_0 \) is the initial population (62 elephants),
- \( r \) is the decay rate (0.04 for 4%),
- \( t \) is the time in years.

Substituting the known values into the equation:

\[
y = 62 (1 - 0.04)^t
\]

This simplifies to:

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

Thus, the correct equation representing the exponential decay of the elephant population is:

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

So, the correct response from the options provided is:

**y equals 62 left parenthesis 0.96 right parenthesis superscript t baseline**.