Question
In an exponential function
y=axb^x
, what does the value of b
represent?
decay factor
initial value
growth factor
dependent variable
y=axb^x
, what does the value of b
represent?
decay factor
initial value
growth factor
dependent variable
Answers
GPT-4o mini
In the exponential function of the form \( y = a \cdot b^x \), the value of \( b \) represents the **growth factor** if \( b > 1 \) or the **decay factor** if \( 0 < b < 1 \).
- If \( b > 1 \): The function models exponential growth, meaning that the value of \( y \) increases as \( x \) increases.
- If \( 0 < b < 1 \): The function models exponential decay, meaning that the value of \( y \) decreases as \( x \) increases.
Thus, the correct answer is that \( b \) can represent either a growth factor or a decay factor, depending on its value. However, if you need to choose one from the options provided, "growth factor" is typically the term used when \( b > 1 \).
- If \( b > 1 \): The function models exponential growth, meaning that the value of \( y \) increases as \( x \) increases.
- If \( 0 < b < 1 \): The function models exponential decay, meaning that the value of \( y \) decreases as \( x \) increases.
Thus, the correct answer is that \( b \) can represent either a growth factor or a decay factor, depending on its value. However, if you need to choose one from the options provided, "growth factor" is typically the term used when \( b > 1 \).