To determine whether the function \( f(x) = 4(0.72)^x \) represents exponential growth or exponential decay, we look at the base of the exponent.
In the function \( f(x) = 4(0.72)^x \):
- The base is \( 0.72 \), which is less than 1.
Since the base is between 0 and 1, this indicates that the function represents exponential decay.
Next, we find the percentage rate of change. For an exponential function of the form \( f(x) = a(b)^x \), where \( 0 < b < 1 \), the percentage rate of change can be calculated as:
\[ \text{Rate of change} = (1 - b) \times 100% \]
For our function, \( b = 0.72 \):
\[ \text{Rate of change} = (1 - 0.72) \times 100% = 0.28 \times 100% = 28% \]
Hence, the function \( f(x) = 4(0.72)^x \) is exponential decay with a percentage rate of change of 28%.
Thus, the correct answer is:
C: Exponential decay; 28%.