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(0.6)^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(0.04)^t

Answer 1

To model the decline of the elephant herd using an exponential decay function, we start with the current population of elephants, which is 62, and recognize that the population will decrease by 4% each year.

An exponential decay function can generally be represented as:

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

where:

• \( y \) is the number of elephants after \( t \) years,
• \( a \) is the initial amount (in this case, 62),
• \( r \) is the rate of decay (in decimal form, so 4% becomes 0.04),
• \( t \) is the time in years.

Since the population is declining by 4%, the remaining percentage of the population each year is 96%, which can be expressed as \( 1 - 0.04 = 0.96 \).

Thus, the function becomes:

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

The correct response from the options given is:

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

This represents the number of elephants after \( t \) years, declining at a rate of 4% annually.