1. Select the options that exemplify exponential decay. a. \( y=1.81(0.79)^{x} \) b. The population of a town decreases \( 10 \% \) every three years. c. \( y=\left(\frac{3}{5}\right)^{x} \) d. \( y=0.79(1.81)^{x} \) e. The population of a town increases \( 3 \% \) every 10 years. f. \( y=\left(\frac{5}{3}\right)^{x} \)

To determine which options exemplify exponential decay, we need to identify the characteristics of exponential decay functions. An exponential decay function typically has the form: \[ y = a \cdot b^x \] where: - \( a > 0 \) (the initial value), - \( 0 < b < 1 \) (the base is a fraction less than 1). Now, let's analyze each option: a. \( y=1.81(0.79)^{x} \) - Here, \( a = 1.81 > 0 \) and \( b = 0.79 < 1 \). This is an example of exponential decay. b. The population of a town decreases \( 10 \% \) every three years. - A decrease of \( 10\% \) means that \( 90\% \) of the population remains, which can be modeled as \( y = a(0.9)^{t} \). This is also an example of exponential decay. c. \( y=\left(\frac{3}{5}\right)^{x} \) - Here, \( a = 1 \) (implied) and \( b = \frac{3}{5} < 1 \). This is an example of exponential decay. d. \( y=0.79(1.81)^{x} \) - Here, \( a = 0.79 > 0 \) and \( b = 1.81 > 1 \). This represents exponential growth, not decay. e. The population of a town increases \( 3 \% \) every 10 years. - An increase of \( 3\% \) means that \( 103\% \) of the population remains, which can be modeled as \( y = a(1.03)^{t} \). This is an example of exponential growth, not decay. f. \( y=\left(\frac{5}{3}\right)^{x} \) - Here, \( a = 1 \) (implied) and \( b = \frac{5}{3} > 1 \). This represents exponential growth, not decay. ### Summary of Exponential Decay Options: - a. \( y=1.81(0.79)^{x} \) - b. The population of a town decreases \( 10 \% \) every three years. - c. \( y=\left(\frac{3}{5}\right)^{x} \) Thus, the options that exemplify exponential decay are **a, b, and c**.