Question
Dorian posted two online videos on the same day.
The total number of views for Video A after t days can be modeled by the equation v = 12t.
The total number of views for Video B after t days is shown by the graph. Which statement is true?
Video B graph of a curve on a coordinate plane that goes up and to the right with time in days on the x axis and total number of views on the y axis. The curve begins at the origin, passes through the point 3 comma 36, and looks like the right half of a U.
The initial value for the function for Video A is greater than the initial value for the function for Video B.
The initial value for the function for Video B is greater than the initial value for the function for Video A.
The rate of change for the function for Video A is constant, but the rate of change for Video B is not constant.
The rate of change for the function for Video B is constant, but the rate of change for Video A is not constant.
The total number of views for Video A after t days can be modeled by the equation v = 12t.
The total number of views for Video B after t days is shown by the graph. Which statement is true?
Video B graph of a curve on a coordinate plane that goes up and to the right with time in days on the x axis and total number of views on the y axis. The curve begins at the origin, passes through the point 3 comma 36, and looks like the right half of a U.
The initial value for the function for Video A is greater than the initial value for the function for Video B.
The initial value for the function for Video B is greater than the initial value for the function for Video A.
The rate of change for the function for Video A is constant, but the rate of change for Video B is not constant.
The rate of change for the function for Video B is constant, but the rate of change for Video A is not constant.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the situation, let's interpret the information provided for both videos.
1. **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.
2. **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:
- **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.
- **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.
- **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.
- **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.**
1. **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.
2. **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:
- **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.
- **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.
- **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.
- **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.**
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