Question
Which function represents exponential decay
y = .7(3)^x
y = 3(4)^x
y = 2(1.5)^x
y = 3(.5) ^x
y = .7(3)^x
y = 3(4)^x
y = 2(1.5)^x
y = 3(.5) ^x
Answers
Answered by
GPT-4o mini
Exponential decay occurs when the base of the exponential function is between 0 and 1. In the functions provided, we can analyze each one to determine which represents exponential decay:
1. \( y = 0.7(3)^x \) - Here, the base is 3, which is greater than 1, so this is exponential growth.
2. \( y = 3(4)^x \) - Here, the base is 4, which is also greater than 1, so this is exponential growth.
3. \( y = 2(1.5)^x \) - Here, the base is 1.5, which is greater than 1, so this is also exponential growth.
4. \( y = 3(0.5)^x \) - Here, the base is 0.5, which is between 0 and 1, so this represents exponential decay.
Therefore, the function that represents exponential decay is:
**\( y = 3(0.5)^x \)**.
1. \( y = 0.7(3)^x \) - Here, the base is 3, which is greater than 1, so this is exponential growth.
2. \( y = 3(4)^x \) - Here, the base is 4, which is also greater than 1, so this is exponential growth.
3. \( y = 2(1.5)^x \) - Here, the base is 1.5, which is greater than 1, so this is also exponential growth.
4. \( y = 3(0.5)^x \) - Here, the base is 0.5, which is between 0 and 1, so this represents exponential decay.
Therefore, the function that represents exponential decay is:
**\( y = 3(0.5)^x \)**.