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 $$ P = 2(1.45)^x $$ to determine which statements are true.

1. **Exponential Growth vs. Decay:**
   - The base of the exponential function is $$ 1.45 $$, which is greater than 1. This indicates that the function models **exponential growth**.
   - **Statement A** is **True**.
   - **Statement B** is **False** because the base is greater than 1, not between 0 and 1.

2. **Initial Amount:**
   - The initial amount of the function is the value of $$ P $$ when $$ x = 0 $$.
   - $$ P(0) = 2(1.45)^0 = 2 	imes 1 = 2 $$.
   - **Statement D** is **True**.
   - **Statement C** is **False** because the initial amount is 2, not 0.45.

3. **Growth Rate:**
   - The standard form of an exponential function is $$ P = P_0(1 + r)^x $$, where $$ r $$ is the growth rate.
   - Comparing $$ 2(1.45)^x $$ to the standard form, $$ 1 + r = 1.45 $$, so $$ r = 0.45 $$ or **45%**.
   - **Statement F** is **True**.
   - **Statement E** is **False** because the rate is 45%, not 1.45%.

**Therefore, the correct statements are A, D, and F.**

**Answer:** All statements A, D, and F are true.
The function $$ P = 2(1.45)^x $$ models **exponential growth**, has an initial amount of **2**, and a growth rate of **45%**. Therefore, statements A, D, and F are true.

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