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(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(0.6)t

Answer 1

To model the decline of the elephant herd, we can use an exponential decay function of the form:

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

where:

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

Since the herd is declining by 4% each year, we can express \( (1 - r) \) as \( (1 - 0.04) = 0.96 \).

Thus, the exponential decay function becomes:

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

Therefore, the correct response is:

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

So the answer is:

y = 62(0.96)^t