Question

Which one of the following functions is an exponential decay function?

A.
f(x) = -2x + 4

B.
f(x) = -x2 - 5

C.
f(x) = 2(0.25)x + 1

D.
f(x) = 3x - 8

Answer 1

An exponential decay function has the general form \( f(x) = a \cdot b^x \) where \( 0 < b < 1 \), and \( a \) is a constant.

Let's analyze the given options:

A. \( f(x) = -2x + 4 \)
- This is a linear function.

B. \( f(x) = -x^2 - 5 \)
- This is a quadratic function.

C. \( f(x) = 2(0.25)^x + 1 \)
- Here, \( b = 0.25 \), which is less than 1. The term \( 2(0.25)^x \) represents exponential decay.

D. \( f(x) = 3x - 8 \)
- This is also a linear function.

Based on this analysis, the exponential decay function is:

**C. \( f(x) = 2(0.25)^x + 1 \)**