A limited-edition poster increases in value each year with an initial value of \( \$ 18 \). After 1 year and an increase of \( 15 \% \) per year, the poster is worth \( \$ 20.70 \). Which equation can be used to find the value, \( y \), after \( x \) years? (Round money values to the nearest penny.) \( \begin{array}{l}y=10(1,15)^{x} \\ y=18(0.15)^{x} \\ y=20.7(1.15)^{x} \\ y=20.7(0.15)^{x} \\ y\end{array} \)

To determine the equation that models the value of the limited-edition poster over time, we'll use the concept of exponential growth. ### Given: - **Initial value ( \( y_0 \) ):** \$18 - **Annual increase rate:** 15% (or 0.15 in decimal form) - **Value after 1 year:** \$20.70 ### Exponential Growth Formula: The general formula for exponential growth is: \[ y = y_0 \times (1 + r)^x \] Where: - \( y \) = value after \( x \) years - \( y_0 \) = initial value - \( r \) = annual growth rate - \( x \) = number of years ### Applying the Values: Plugging the given values into the formula: \[ y = 18 \times (1 + 0.15)^x \] \[ y = 18 \times (1.15)^x \] ### Verification: After 1 year (\( x = 1 \)): \[ y = 18 \times 1.15 = 20.70 \] This matches the value provided, confirming the correctness of the equation. ### Conclusion: The appropriate equation to model the value of the poster after \( x \) years is: \[ y = 18 \times (1.15)^x \] **Answer:** \[ y = 18 \times (1.15)^x \]