Maria created a graph of B(t), the temperature over time. For the interval between t = 3 and t = 7, the average rate of change in her graph of B(t) is 8. Which statement must be true?
the third one
Temperature was 32. Plug in 32.
8=32/(7-3)
B(t) rose by 32
The temperature was 8 degrees higher when t = 7 than when t = 3.
The temperature was 8 times higher when t = 7 than when t = 3.
The temperature was 32 degrees higher when t = 7 than when t = 3.
The temperature was 2 degrees higher when t = 7 than when t = 3.
temperature was 8 time higher when t=7 when t=3
the fourth one
To determine which statement must be true, we can use the formula for average rate of change, which is given by:
Average rate of change = (change in temperature) / (change in time)
In this case, we are given that the average rate of change in the graph of B(t) between t = 3 and t = 7 is 8. So we can set up the equation as follows:
8 = (B(7) - B(3)) / (7 - 3)
Now, we can consider the options and check if they satisfy this equation:
1. B(3) = 8 and B(7) = 16: We substitute these values into the equation:
8 = (16 - 8) / (7 - 3)
8 = 8 / 4
8 = 2
Since the equation does not hold true, we can conclude that statement 1 is not true.
2. B(3) = 12 and B(7) = 28: Again, we substitute these values into the equation:
8 = (28 - 12) / (7 - 3)
8 = 16 / 4
8 = 4
Once again, the equation does not hold true, so statement 2 is not true either.
3. B(3) = -4 and B(7) = 44: Substituting these values into the equation:
8 = (44 - (-4)) / (7 - 3)
8 = 48 / 4
8 = 12
The equation does not hold true, so statement 3 is not true.
From this analysis, we can conclude that none of the given statements are true because none of them satisfy the equation for the average rate of change.