Which equation represents exponential decay?
a: f(x)= 8^x
b: f(x) = 0.08^x
c: f(x) = 0.2(4)^x
d: f(x) = 5(2)^x
The correct equation that represents exponential decay is b: f(x) = 0.08^x.
The equation that represents exponential decay is b: f(x) = 0.08^x.
To determine which equation represents exponential decay, we need to understand the characteristics of exponential functions.
Exponential decay occurs when a value decreases rapidly over time. In an exponential function representing decay, the base should be a value between 0 and 1. The exponent will be positive since we are looking at decay.
Let's analyze the given options:
a: f(x) = 8^x - This equation represents exponential growth because the base (8) is greater than 1.
b: f(x) = 0.08^x - This equation represents exponential decay as the base (0.08) is between 0 and 1.
c: f(x) = 0.2(4)^x - This equation represents exponential growth because the base (4) is greater than 1.
d: f(x) = 5(2)^x - This equation represents exponential growth because the base (2) is greater than 1.
Based on the analysis, option b, f(x) = 0.08^x, represents exponential decay because it fulfills the criteria of having a base between 0 and 1.