3) A website heis 300,000 members. the number of Members (y) increases by \( 11 \% \) each year. select all that apply d(A. this situation can Be modeled by the equation \( 1=300,000(1.11)^{+} \) B. B. 0 this situation can be modeled by the equation \( 300,000(0,11)^{+} \) Y=300,000 (0.11) Y. It this sitation cain be modered by the equation \( Y=0.11(300,000)^{t} \) D. Ithere will Be approximately 33,000 members after 4 years Be a E. a thene w after 4 years F. I there will be approximately 455000 members after 4 years

Let's analyze each of the provided options based on the information that the website starts with **300,000 members** and the number of members increases by **11% each year**. ### 1. **Modeling the Situation** To model the growth of members, we use the **exponential growth formula**: \[ Y(t) = Y_0 \times (1 + r)^t \] Where: - \( Y(t) \) is the number of members after \( t \) years. - \( Y_0 \) is the initial number of members. - \( r \) is the growth rate (expressed as a decimal). - \( t \) is the time in years. Given: - \( Y_0 = 300,000 \) - \( r = 11\% = 0.11 \) So, the correct model is: \[ Y(t) = 300,000 \times (1.11)^t \] ### 2. **Evaluating the Options** Let's evaluate each option based on the correct model. #### **Option A** > **A.** This situation can be modeled by the equation \( Y = 300,000(1.11)^t \). **Evaluation:** *Correct.* This matches the exponential growth model correctly. #### **Option B** > **B.** This situation can be modeled by the equation \( Y = 300,000(0.11)^t \). > \( Y = 300,000 \times 0.11 \) **Evaluation:** *Incorrect.* Using \( 0.11 \) as the base of the exponent implies a decay model, which is not appropriate here. #### **Option C** > **C.** This situation can be modeled by the equation \( Y = 0.11(300,000)^t \). **Evaluation:** *Incorrect.* This incorrectly applies the growth rate and misplaces the initial value in the exponent. #### **Option D** > **D.** There will be approximately 33,000 members after 4 years. **Evaluation:** *Incorrect.* Starting with 300,000 members and increasing by 11% each year, the number of members after 4 years is much higher. #### **Option F** > **F.** There will be approximately 455,000 members after 4 years. **Evaluation:** *Correct.* **Calculation:** \[ Y(4) = 300,000 \times (1.11)^4 \approx 300,000 \times 1.5171 \approx 455,130 \] ### **Summary of Correct Options** - **A.** Correct - **F.** Correct All other options are either incorrect or incomplete. **Final Answer:** **Options A and F are correct.**