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

y=62(0.6)t

Answer 1

To model the decline of the herd of elephants at a rate of 4% per year, we can use the exponential decay function. The general form for exponential decay is:

\[ y = y_0 e^{-kt} \]

where:

• \( y \) is the quantity after time \( t \),
• \( y_0 \) is the initial quantity,
• \( k \) is the decay constant, and
• \( t \) is the time in years.

However, since we want to express the function in terms of a simpler model:

The herd is declining by 4% each year, which means that 96% of the herd remains each year. We can express this as:

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

In this case, \( 62 \) is the initial number of elephants, \( 0.96 \) represents the remaining percentage of the herd each year (100% - 4% = 96%), and \( t \) is the number of years.

Therefore, the correct function is:

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

So the answer is:

y = 62(0.96)^t