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

y=78(0.09)t
y equals 78 left parenthesis 0.09 right parenthesis superscript t baseline

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

y=78(1.09)t

Answer 1

To model the decline of a cackle of hyenas that decreases by 9% each year, you can use the exponential decay function of the form:

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

where:
- \( y_0 \) is the initial amount,
- \( r \) is the rate of decay (as a decimal),
- \( t \) is the time in years,
- \( y \) is the amount remaining after \( t \) years.

Given:
- The initial number of hyenas \( y_0 = 78 \),
- The rate of decay \( r = 0.09 \) (9%).

Therefore, the function becomes:

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

This simplifies to:

\[ y = 78 (0.91)^t \]

Thus, the correct exponential decay function to model this problem is:

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