(1990,52),(1992,55),(1994,59),
(1996,63),(1998,66)
With out calculating find a 2-year period that had a greater rate of chsnge than 1990-1992 explain your reasoning
Well, rate of change = slope
deltaY/deltX = slope
deltaY = (y2-y1)
deltaX =(x2-x1)
For the year 1990-1992:
deltaY = (55-52) = 3
deltaX =(1992-1990) = 2
3/2 = 1.5=slope
So basically, you have to pick 2 years where
deltaY > 3
deltaY <= 2
so the only years that meet those conditions are
1994-1996
To determine a 2-year period with a greater rate of change than 1990-1992, we need to compare the rate of change between each set of consecutive years.
The rate of change can be found by taking the difference in the values of the corresponding years and dividing it by the number of years. In this case, we will consider the difference in the second year's value and the first year's value, divided by 2, since we are looking at a 2-year period.
Let's calculate the rates of change for each 2-year period:
- 1990-1992: (55-52)/2 = 1.5
- 1992-1994: (59-55)/2 = 2
- 1994-1996: (63-59)/2 = 2
- 1996-1998: (66-63)/2 = 1.5
Comparing the rates of change, we find that both the 1992-1994 and 1994-1996 periods have a greater rate of change than the 1990-1992 period. This is because their rates of change are both equal to 2, while the rate of change for 1990-1992 is 1.5.
Therefore, the 1992-1994 and 1994-1996 periods have a greater rate of change than the 1990-1992 period.