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 $$ 45 \% $$.

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Let's analyze the exponential function $$ P = 2(1.45)^x $$ and evaluate each statement:

**A. This function models exponential growth.**  
- **True.**  
  The base of the exponential function is $$ 1.45 $$, which is greater than 1. This indicates that the function represents exponential growth.

**B. This function models exponential decay.**  
- **False.**  
  Exponential decay would require the base to be between 0 and 1. Since $$ 1.45 > 1 $$, it does not model decay.

**C. The initial amount is 0.45.**  
- **False.**  
  The initial amount is determined by the value of $$ P $$ when $$ x = 0 $$.  
  $$ P(0) = 2(1.45)^0 = 2 	imes 1 = 2 $$.

**D. The initial amount is 2.**  
- **True.**  
  As calculated above, the initial amount $$ P(0) $$ is 2.

**E. The rate is $$ 1.45\% $$.**  
- **False.**  
  The rate is represented by $$ r $$ in the expression $$ P = P_0(1 + r)^x $$. Here, $$ 1 + r = 1.45 $$, so $$ r = 0.45 $$ or $$ 45\% $$.

**F. The rate is $$ 45\% $$.**  
- **True.**  
  As calculated above, the rate $$ r = 45\% $$.

**Summary of True Statements:**  
- **A. This function models exponential growth.**  
- **D. The initial amount is 2.**  
- **F. The rate is $$ 45\% $$.**

Answer: All statements A, D, and F are true.
The function $$ P = 2(1.45)^x $$ models exponential growth, the initial amount is 2, and the rate is 45%.

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