Question

question 24 (mandatory) (1 point) does y = 0.5^x represent exponential growth or decay? how do you know?

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = a\cdot b^{x}$, where $a
eq0$, $b > 0$ and $b
eq1$. In the function $y = 0.5^{x}$, $a = 1$ and $b=0.5$.

Step2: Determine growth or decay

If $b> 1$, the function represents exponential growth. If $0 < b<1$, the function represents exponential decay. Since $0<0.5 < 1$, the function $y = 0.5^{x}$ represents exponential decay.

Answer:

The function $y = 0.5^{x}$ represents exponential decay because the base $b = 0.5$ and $0<0.5<1$.