Question
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
Answers
GPT-4o mini
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:
- \( y = 0.25^x \)
- \( y = 500(1/2)^x \)
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:
- \( y = 0.25^x \)
- \( y = 500(1/2)^x \)