If a YouTube video gets shared, the number of views grows exponentially with time. Julia models this phenomenon with the function V(t)=4(1.5)^t, where t is the number of days since the video was uploaded. Which of the following statements about Julia's function is true? 
Options:
A. The video initially had 4 views. 
B. The number of views increases by 1.5 times each day. 
C. At each interval, the number of views doubles. 
D. The video can reach a maximum of 4 views.

To analyze the given exponential function \( V(t) = 4(1.5)^t \), let's break it down step-by-step and understand what each part represents:

1. **Understanding the Function:**

   The function \( V(t) = 4(1.5)^t \) describes the number of views \( V(t) \) on a video \( t \) days after it has been uploaded. Here:
   - The coefficient **4** represents the **initial number of views** at \( t = 0 \).
   - The base **1.5** is the **growth factor**, which tells us that the number of views grows by a factor of 1.5 each day.

2. **Analyzing Each Statement:**

   Let's consider each option:

   **Option A: The video initially had 4 views.**

   - This is **true** because when \( t = 0 \):
     \[
     V(0) = 4(1.5)^0 = 4 \times 1 = 4.
     \]
     Thus, the initial number of views is indeed 4.

   **Option B: The number of views increases by 1.5 times each day.**

   - This is **true**. The base of the exponential function, 1.5, represents the daily growth factor, meaning the number of views increases by 1.5 times each day.

   **Option C: At each interval, the number of views doubles.**

   - This is **false**. The number of views increases by 1.5 times, not doubles. Doubling would require a growth factor of 2.

   **Option D: The video can reach a maximum of 4 views.**

   - This is **false**. Since the function is exponential with a growth factor greater than 1, the number of views will continue to increase indefinitely, and there is no maximum limit.

3. **Conclusion:**

   The correct statements about Julia's function are:

   - **Option A: The video initially had 4 views.**
   - **Option B: The number of views increases by 1.5 times each day.**

Would you like more details or have any questions? Here are some related questions:

1. How would the function change if the growth factor was doubled?
2. What would the view count be after 5 days?
3. How does changing the initial number of views affect the function?
4. What is the significance of the base in an exponential growth function?
5. How would the graph of this function look?

**Tip:** For exponential functions, the base represents the growth rate, and the initial value is the starting point when \( t = 0 \).

If a YouTube video gets shared, the number of views grows exponentially with time. Julia models this phenomenon with the function V(t) = 4(1.5)^t, where t is the number of days since the video was uploaded. Which of the following statements about Julia's function is true?

Explore how exponential functions model the growth of YouTube views over time with the function V(t) = 4(1.5)^t. This problem covers key concepts like initial value, growth rate, and exponential growth, suitable for students in Grades 9-11.

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