14) An exponential function can be modeled by the function \( P=2(1.45)^{x} \). Which of the following statements is true? Select all that apply. A. \( \square \) This function models exponential growth. B. \( \square \) This function models exponential decay. C. \( \square \) The initial amount is 0.45 . D. \( \square \) The initial amount is 2 . E. \( \square \) The rate is \( 1.45 \% \). F. \( \square \) The rate is \( 45 \% \).

Let's analyze the given exponential function: \[ P = 2(1.45)^x \] This function is in the form \( P = a \cdot b^x \), where: - \( a = 2 \) is the **initial amount** (value of \( P \) when \( x = 0 \)). - \( b = 1.45 \) is the **growth factor**. Now, let's evaluate each statement: **A. \( \square \) This function models exponential growth.** - **True.** Since the base \( b = 1.45 \) is greater than 1, the function represents exponential growth. **B. \( \square \) This function models exponential decay.** - **False.** Exponential decay occurs when \( 0 < b < 1 \). Here, \( b = 1.45 > 1 \), indicating growth, not decay. **C. \( \square \) The initial amount is 0.45.** - **False.** The initial amount \( a \) is 2, not 0.45. The 0.45 might be confused with the growth component of \( b \), but it does not represent the initial amount. **D. \( \square \) The initial amount is 2.** - **True.** As identified, \( a = 2 \) is the initial amount. **E. \( \square \) The rate is \( 1.45\% \).** - **False.** The growth rate is determined by \( b = 1.45 \). To find the percentage growth rate, subtract 1 from the growth factor: \( 1.45 - 1 = 0.45 \), which is 45%, not 1.45%. **F. \( \square \) The rate is \( 45\% \).** - **True.** As calculated above, the growth rate is 45%. **Summary of True Statements:** - **A. This function models exponential growth.** - **D. The initial amount is 2.** - **F. The rate is \( 45\% \).** **Final Answer:** **All statements A, D, and F are true.**