Question 1 (1 point) What is the rate of growth or rate of decay? \[ y=5575(0.65)^{x} \] a \( x \) b 5575 c \( \quad .65 \) d 1

To determine the rate of growth or decay from the given equation \( y = 5575(0.65)^{x} \), we need to analyze the base of the exponential function. 1. **Identify the components of the equation:** - The equation is in the form \( y = a(b)^{x} \), where: - \( a = 5575 \) (the initial value) - \( b = 0.65 \) (the base of the exponential function) 2. **Determine the nature of the base \( b \):** - If \( b < 1 \), the function represents exponential decay. - If \( b > 1 \), the function represents exponential growth. In this case, since \( b = 0.65 \), which is less than 1, the function represents exponential decay. 3. **Calculate the rate of decay:** - The rate of decay can be found using the formula \( r = 1 - b \). - Here, \( r = 1 - 0.65 = 0.35 \). Thus, the rate of decay is 0.35, which indicates that the function decreases by 35% for each unit increase in \( x \). **Final Answer:** The correct option that represents the rate of decay is: - c \( 0.65 \) (indicating the decay factor, but the rate of decay itself is \( 0.35 \)). However, if we are strictly looking for the decay factor, the answer is \( 0.65 \).