\[ t \geq 0 \] 6 Milliple Cholce 10 points Write an equation that models the following siluation Samantha's hair was known to grow very rapidly il began at a length ef 6 in and grow at a rate of 145 a wock \[ \begin{array}{l} y=6(1.14)^{z} \\ y=6(1+14)^{2} \\ y=6(0.14)^{x} \\ y=6(0.86)^{2} \end{array} \]

To model Samantha's hair growth, we need to establish an exponential growth equation based on the given information: 1. **Initial Length**: Samantha's hair starts at 6 inches. 2. **Growth Rate**: Her hair grows at a rate of 14.5% per week (assuming "145 a wock" was a typographical error and should be "14.5% per week"). The general form of an exponential growth equation is: \[ y = y_0 (1 + r)^t \] Where: - \( y \) = future length of the hair - \( y_0 \) = initial length (6 inches) - \( r \) = growth rate per time period (14.5% or 0.145) - \( t \) = number of time periods (weeks) Plugging in the values: \[ y = 6(1 + 0.145)^t = 6(1.145)^t \] Among the provided options, the closest correct model is: \[ y = 6(1.14)^z \] This equation represents the hair growing from an initial length of 6 inches at an approximate growth rate of 14% per time period \( z \). **Correct Equation:** \[ y = 6(1.14)^{z} \]