Which of the following represent exponential decay? Select all that apply. (1 point) Responses y=0.25x y is equal to 0 point 2 5 to the x th power y=500(12)x y is equal to 500 times 1 half to the x th power y=0.25x+3 y=0.25x+3 y=30(1.5)x y is equal to 30 times 1 point 5 to the x th power

Answer 1

To identify which equations represent exponential decay, we look for equations in the form \( y = a \cdot b^x \) where \( 0 < b < 1 \) (indicating decay).

Let's evaluate the provided options:

1. \( y = 0.25^x \):

   • Here, \( b = 0.25 \) (which is less than 1). This represents exponential decay.

2. \( y = 500(1/2)^x \):

   • Here, \( b = \frac{1}{2} \) (which is less than 1). This represents exponential decay.

3. \( y = 0.25x + 3 \):

   • This is a linear equation, not an exponential function. It does not represent exponential decay.

4. \( y = 30(1.5)^x \):

   • Here, \( b = 1.5 \) (which is greater than 1). This represents exponential growth, not decay.

Summary of Results:

The functions that represent exponential decay from the given options are:

• \( y = 0.25^x \)
• \( y = 500(1/2)^x \)