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 equals 62 left parenthesis 0.96 right parenthesis superscript t baseline
y=62(0.04)t
y equals 62 left parenthesis 0.04 right parenthesis superscript t baseline
y=62(0.6)t
y equals 62 left parenthesis 0.6 right parenthesis superscript t baseline
y=62(1.04)t

Answer 1

To model the decline of the elephant herd, we can use the formula for exponential decay, which is given by:

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

Where:

• \( y_0 \) is the initial quantity (62 elephants in this case),
• \( r \) is the decay rate (4% or 0.04),
• \( t \) is the time in years.

Since the herd is declining at a rate of 4% per year, \( (1 - r) \) would be \( 1 - 0.04 = 0.96 \).

So the exponential decay function can be written as:

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

Therefore, the correct response is:

y = 62(0.96)^t