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

0 y = 62(1.04)*
0 y = 62(0.04) *
0 y = 62(0.96) *
0 y = 62(0.6) *

Answer 1

To model the decline of the elephant herd using an exponential decay function, we need to consider the rate of decline and the initial number of elephants.

Given:

• The initial number of elephants: \( y_0 = 62 \)
• The rate of decline: 4% per year

In exponential decay, the function can be represented as:

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

Where:

• \( y \) is the number of elephants after \( t \) years,
• \( y_0 \) is the initial amount (62 elephants),
• \( r \) is the rate of decay (0.04 for 4%),
• \( t \) is the time in years.

Thus, substituting in the values we have:

\[ y = 62 \times (1 - 0.04)^t \] \[ y = 62 \times (0.96)^t \]

So, the correct exponential decay function to model the problem is:

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

Thus, the correct option is:

**0 y = 62(0.96) ***