Question

Which equation represents exponential decay?

answers below:

f (z) = 8^x

f (z) = 0.08^x

f (z) = 0.2(4)^x

f (z) = 5(2)^x

Answer 1

Exponential decay occurs when the base of the exponential function is between 0 and 1.

Let's analyze the given equations:

1. \( f(z) = 8^x \) - This represents exponential growth since the base (8) is greater than 1.
2. \( f(z) = 0.08^x \) - This represents exponential decay since the base (0.08) is between 0 and 1.
3. \( f(z) = 0.2(4)^x \) - This represents growth as \(4^x\) grows, although the \(0.2\) multiplies it, it doesn't change the fact that \(4^x\) grows.
4. \( f(z) = 5(2)^x \) - This represents growth since the base (2) is greater than 1.

Thus, the equation that represents exponential decay is **\( f(z) = 0.08^x \)**.