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 exponential decay function. The general form of an exponential decay function is given by:

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

where:

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

Since the herd is declining at a rate of 4% per year, we can express the function as:

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

Therefore, the correct exponential decay function is:

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

So the appropriate response is:

y = 62(0.96)^t