Question

A group of hyenas is called a cackle. In a certain geographic location, a cackle of hyenas is declining at a rate of nine percent every year. If there are currently 78 hyenas in the cackle, create an exponential decay function to model the problem.(1 point)
Responses

y=78(0.9)t
y equals 78 left parenthesis 0.9 right parenthesis superscript t baseline

y=78(0.91)t
y equals 78 left parenthesis 0.91 right parenthesis superscript t baseline

y=78(1.09)t
y equals 78 left parenthesis 1.09 right parenthesis superscript t baseline

y=78(0.09)t

Answer 1

To create an exponential decay function for the decline of a cackle of hyenas, we start with the initial population and the decay rate.

In this case, the initial population of hyenas is 78, and the population is declining at a rate of 9% per year.

To represent this decline using an exponential decay function, we can use the formula:

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

where:
- \( A \) is the initial amount (78 hyenas),
- \( r \) is the rate of decay (9% or 0.09),
- \( t \) is the time in years.

So, we can plug the values into the formula:

\[ y = 78(1 - 0.09)^t \]
\[ y = 78(0.91)^t \]

Thus, the correct exponential decay function that models the decline of the hyenas is:

**y = 78(0.91)^t**