Question

Which of the following functions represent exponential decay?

y = 2^x
y = -2^x
7 = 2^0.5x
y = (1/2)^x

Answer 1

Exponential decay occurs when the base b in y = a·b^x satisfies 0 < b < 1 (so the value decreases as x increases).

- y = 2^x: base 2 > 1 → exponential growth, not decay.
- y = -2^x: base 2 > 1, and the negative sign flips the sign (values become more negative as x increases). Its magnitude grows, so this is not exponential decay.
- 7 = 2^0.5x: as written this is an equation (not a function). If you meant y = 2^{0.5x} then the effective base is 2^{0.5} = √2 > 1 → growth, not decay.
- y = (1/2)^x: base 1/2 is between 0 and 1 → exponential decay.

So, only y = (1/2)^x represents exponential decay.