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)

Question

Responses

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

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

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

y=62(1.04)t

Answer 1

To model the decline of the herd of elephants using an exponential decay function, we can start with the initial number of elephants, which is 62. The herd declines at a rate of 4% per year. This means that each year, 96% of the elephants remain (100% - 4% = 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 rate of decay (0.04 for 4%),
• \(t\) is the time in years.

This can be simplified to:

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

Thus, the correct exponential decay function is:

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

So the correct response is:

y = 62(0.96)^t