To analyze the situation, let's interpret the information provided for both videos.
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Video A: The equation for the total number of views after \( t \) days is given by \( v = 12t \). This indicates that:
- The initial value (at \( t = 0 \)) is \( v(0) = 12 \times 0 = 0 \).
- The rate of change is constant at 12 views per day.
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Video B: The graph starts at the origin (0,0) and passes through the point (3, 36), which means:
- The initial value (at \( t = 0 \)) is \( v(0) = 0 \).
- The total number of views at \( t = 3 \) days is 36, but we do not have specific data about the rate of change throughout the entire duration from the graph directly.
Now, let's evaluate the statements:
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Statement 1: “The initial value for the function for Video A is greater than the initial value for the function for Video B.”
- Video A's initial value is 0 and Video B's initial value is also 0. This statement is false.
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Statement 2: “The initial value for the function for Video B is greater than the initial value for the function for Video A.”
- Both initial values are equal (0). This statement is false.
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Statement 3: “The rate of change for the function for Video A is constant, but the rate of change for Video B is not constant.”
- For Video A, the rate of change is constant at 12 views per day. For Video B, since the graph looks like the right half of a U, the rate of change is increasing initially (as it rises) and then could potentially decrease, indicating that it is not constant. This statement is true.
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Statement 4: “The rate of change for the function for Video B is constant, but the rate of change for Video A is not constant.”
- This is false, as we determined that the rate of change for Video A is constant.
Given this analysis, the true statement is:
The rate of change for the function for Video A is constant, but the rate of change for Video B is not constant.