Question
Which equations and graphs represent exponential decay?
(TIP: Us
a b c or d
(TIP: Us
a b c or d
Answers
GPT-4o mini
To identify which equations and graphs represent exponential decay, you should look for characteristics of the exponential decay function. The standard form of an exponential decay function can be represented as:
\[ y = a \cdot e^{-bx} \]
where:
- \( a > 0 \) (the initial value),
- \( b > 0 \) (the decay constant).
In terms of graphs, an exponential decay curve will start at a positive value (if \( a > 0 \)) and will steadily decrease towards zero as \( x \) increases, never actually reaching zero.
If you're given options (a, b, c, d), look for:
1. **Equations** that follow the form \( y = a \cdot e^{-bx} \) or \( y = a \cdot (1 - r)^t \) with \( r > 0 \).
2. **Graphs** that show a smooth curve starting from a high value and approaching the x-axis but never touching it as \( x \) increases.
If you can provide the specific options (a, b, c, d), I can help determine which represent exponential decay.
\[ y = a \cdot e^{-bx} \]
where:
- \( a > 0 \) (the initial value),
- \( b > 0 \) (the decay constant).
In terms of graphs, an exponential decay curve will start at a positive value (if \( a > 0 \)) and will steadily decrease towards zero as \( x \) increases, never actually reaching zero.
If you're given options (a, b, c, d), look for:
1. **Equations** that follow the form \( y = a \cdot e^{-bx} \) or \( y = a \cdot (1 - r)^t \) with \( r > 0 \).
2. **Graphs** that show a smooth curve starting from a high value and approaching the x-axis but never touching it as \( x \) increases.
If you can provide the specific options (a, b, c, d), I can help determine which represent exponential decay.