Question

Which function represents exponential decay?

a) f(x) = 2^x
b) f(x) = 3^x
c) f(x) = 3(2)^x
d) f(x) = 2^(-1)

Answer 1

The function that represents exponential decay is f(x) = 2⁻¹. Hence, d) is correct.

Step-by-step explanation:

The function that represents exponential decay is f(x) = 2⁻¹

An exponential decay function is a function that decreases at a constant rate. In this case, the base of the function is 2 raised to the power of -1, which means it decreases by half every time x increases by 1.

For example, when x = 1, f(x) = 2⁻¹ = 1/2. When x = 2, f(x) = 2⁻² = 1/4. And so on.