1.what kind of function best models the data in the table use differences and ratios.
x y
0 5
1 7
2 9
3 11
4 13
2.write an equation to model the data table.
x y
0 3
1 5.3
2 7.6
3 9.9
4 12.2
3.write an equation to model the data table.
x y
0 1.4
1 4.2
2 12.6
3 37.8
4 113.4
Help... ASAP
1. note constant d = 2
arithmetic sequence
straight line of slope 2
2. constant d again
y = m x + b
y = 2.3 x + 3
3, whoa, climbing faster
try
y(n+1) = 3 y(n)
geometric
ratio is always 3
or r = 3
y = 1.4 * 3^(x)
try x = 4
y = 1.4 * 3^4 = 1.4 * 81 = 113.4
it worked
1. To determine the best kind of function that models the data in the table using differences and ratios, we can look for patterns in the differences between consecutive values of y and the ratios between consecutive values of y.
Let's calculate the differences between consecutive values of y:
7 - 5 = 2
9 - 7 = 2
11 - 9 = 2
13 - 11 = 2
The differences between consecutive values of y are all 2, which suggests a linear relationship.
Now, let's calculate the ratios between consecutive values of y:
7 / 5 = 1.4
9 / 7 = 1.2857..
11 / 9 = 1.2222..
13 / 11 = 1.1818..
The ratios between consecutive values of y are approximately constant but decreasing slightly. This suggests a linear relationship as well.
Based on the patterns in both the differences and ratios, a linear function (y = mx + b) would be the best kind of function to model the data in the table.
2. To write an equation to model the data table:
The first step is to determine the slope (m) and y-intercept (b) of the linear function.
Using any two data points (x1, y1) and (x2, y2), we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose (0, 3) and (1, 5.3) as the two points:
m = (5.3 - 3) / (1 - 0) = 2.3 / 1 = 2.3
Now we can substitute the slope (m) and one of the points (x1, y1) into the slope-intercept form (y = mx + b) to find the y-intercept (b):
3 = 2.3 * 0 + b
b = 3
Therefore, the equation that models the data table is:
y = 2.3x + 3
3. To write an equation to model the data table:
Following the same steps as before, let's calculate the slope (m) and y-intercept (b) of the linear function.
Using the points (0, 1.4) and (1, 4.2):
m = (4.2 - 1.4) / (1 - 0) = 2.8 / 1 = 2.8
Using the point (0, 1.4) to find the y-intercept:
1.4 = 2.8 * 0 + b
b = 1.4
Therefore, the equation that models the data table is:
y = 2.8x + 1.4