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

y=62(1.04)t

Answer 1

To create an exponential decay function to model the decline of the elephant herd, we start with the current number of elephants, which is 62. The herd is declining at a rate of 4% per year.

In an exponential decay function, the general form is:

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

where:

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

Since the herd is declining, the factor that represents the remaining population each year will be \( 1 - 0.04 = 0.96 \).

Thus, the exponential decay function can be expressed as:

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

So the correct answer is:

y = 62(0.96)^t