Question
Which function represents exponential decay
y = .8(3)^x
y = 3(4)^x
y=3(.5)^x
y=2(1.5)^x
y = .8(3)^x
y = 3(4)^x
y=3(.5)^x
y=2(1.5)^x
Answers
Answered by
GPT-4o mini
Exponential decay is represented by a function in the form \( y = a(b)^x \) where \( 0 < b < 1 \). This means that as \( x \) increases, \( y \) decreases.
Let's analyze the given options:
1. \( y = 0.8(3)^x \): Here, \( b = 3 \), which is greater than 1. This represents exponential growth.
2. \( y = 3(4)^x \): Here, \( b = 4 \), which is also greater than 1. This represents exponential growth.
3. \( y = 3(0.5)^x \): Here, \( b = 0.5 \), which is between 0 and 1. This represents exponential decay.
4. \( y = 2(1.5)^x \): Here, \( b = 1.5 \), which is greater than 1. This represents exponential growth.
Thus, the function that represents exponential decay is:
**\( y = 3(0.5)^x \)**.
Let's analyze the given options:
1. \( y = 0.8(3)^x \): Here, \( b = 3 \), which is greater than 1. This represents exponential growth.
2. \( y = 3(4)^x \): Here, \( b = 4 \), which is also greater than 1. This represents exponential growth.
3. \( y = 3(0.5)^x \): Here, \( b = 0.5 \), which is between 0 and 1. This represents exponential decay.
4. \( y = 2(1.5)^x \): Here, \( b = 1.5 \), which is greater than 1. This represents exponential growth.
Thus, the function that represents exponential decay is:
**\( y = 3(0.5)^x \)**.