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

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

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

y=62(0.96)t

Answer 1

The correct exponential decay function to model the decline of the elephant population is:

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

Here's the reasoning:

• The current population is 62 elephants.
• The herd is declining at a rate of 4% per year, which means that 96% of the population remains after each year. This is represented as \( 1 - 0.04 = 0.96 \).
• Therefore, the number of elephants after \( t \) years can be modeled by the function:

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