Question

In a certain flock of pigeons, the population is declining at a rate of 5% per year. If there are currently 140 pigeons in the flock, create an exponential decay function to model the problem. Let y represent the number of pigeons after x years. (1 point) Responses y=140(0.95)x y is equal to 140 times 0 point 9 5 to the x th power y=140(1.05)x y is equal to 140 times 1 point 0 5 to the x th power y=140(0.05)x y is equal to 140 times 0 point 0 5 to the x th power y=140(0.5)x

Answer 1

To create an exponential decay function for the flock of pigeons, we start with the initial population and the decay rate.

Given:
- Initial population, \( P_0 = 140 \) pigeons
- Decay rate = 5% per year, or 0.05 as a decimal

The population after \( x \) years can be modeled using the exponential decay function:

\[
y = P_0 \times (1 - \text{decay rate})^x
\]

Substituting the initial population and decay rate:

\[
y = 140 \times (1 - 0.05)^x
\]
\[
y = 140 \times (0.95)^x
\]

Thus, the correct exponential decay function is:

\[
y = 140(0.95)^x
\]

So, the appropriate response is:

**y = 140(0.95)^x**