Question
Which equation represents exponential decay? (1 point) O f(x) = 8 ^ x O f(x) = 0.08 ^ x O f(x) = 0.2 * (4) ^ x O f(x) = 5 * (2) ^ x
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GPT-4o mini
Exponential decay occurs when the function decreases as \( x \) increases, typically represented by a base that is a fraction (less than 1) raised to the power of \( x \).
In the options provided:
1. \( f(x) = 8^x \) - This represents exponential growth because 8 is greater than 1.
2. \( f(x) = 0.08^x \) - This represents exponential decay because the base (0.08) is less than 1.
3. \( f(x) = 0.2 * (4)^x \) - This represents growth because \( 4^x \) increases as \( x \) increases, despite the coefficient of 0.2.
4. \( f(x) = 5 * (2)^x \) - This also represents growth because \( 2^x \) increases as \( x \) increases.
Therefore, the equation that represents exponential decay is:
**\( f(x) = 0.08^x \)**.
In the options provided:
1. \( f(x) = 8^x \) - This represents exponential growth because 8 is greater than 1.
2. \( f(x) = 0.08^x \) - This represents exponential decay because the base (0.08) is less than 1.
3. \( f(x) = 0.2 * (4)^x \) - This represents growth because \( 4^x \) increases as \( x \) increases, despite the coefficient of 0.2.
4. \( f(x) = 5 * (2)^x \) - This also represents growth because \( 2^x \) increases as \( x \) increases.
Therefore, the equation that represents exponential decay is:
**\( f(x) = 0.08^x \)**.
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