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:
- Equations that follow the form \( y = a \cdot e^{-bx} \) or \( y = a \cdot (1 - r)^t \) with \( r > 0 \).
- 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.
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