Select the best description of the following exponential equation. \( f(x)=19(3.52)^{x} \) Show your work here Decaying by \( 252 \% \) with every unit of \( x \). Decaying by \( 352 \% \) with every unit of \( x \). Growing by \( 352 \% \) with every unit of \( x \). Growing by \( 252 \% \) with every unit of \( x \).

To determine the best description of the exponential equation: \[ f(x) = 19(3.52)^x \] we need to analyze the components of the equation and understand how they contribute to its behavior. ### Step 1: Identify the General Form The given equation is in the general exponential form: \[ f(x) = a \cdot b^x \] where: - \( a = 19 \) is the initial value (the value of \( f(x) \) when \( x = 0 \)). - \( b = 3.52 \) is the base of the exponential function, which determines the growth or decay rate. ### Step 2: Determine Growth or Decay - **If \( b > 1 \)**: The function represents **exponential growth**. - **If \( 0 < b < 1 \)**: The function represents **exponential decay**. In this case, \( b = 3.52 \), which is greater than 1. Therefore, the function exhibits **exponential growth**. ### Step 3: Calculate the Percentage Growth Rate The percentage growth rate for an exponential function is calculated using the formula: \[ \text{Growth Rate (\%)} = (b - 1) \times 100\% \] Plugging in the value of \( b \): \[ \text{Growth Rate (\%)} = (3.52 - 1) \times 100\% = 2.52 \times 100\% = 252\% \] This means that for every unit increase in \( x \), the function \( f(x) \) grows by **252\%**. ### Conclusion Based on the calculations: - The function \( f(x) = 19(3.52)^x \) **grows** because the base \( 3.52 \) is greater than 1. - The growth rate is **252\%** per unit increase in \( x \). **Therefore, the best description is:** **Growing by \( 252\% \) with every unit of \( x \).**