Which kind of function best models the data in the table? Use differences or ratios.
X = 0, y = 1.7
x = 1, y = 6.8
x = 2, y = 27.2
x = 3, y = 108.8
x = 4, y = 435.2
Can you please help me with this? I do not understand this unit as well as the other ones.
I forgot to put the answers:
A) linear
B) quadratic
C) exponential
D) none of the above
To determine which kind of function best models the data in the table, we can examine the differences or ratios between consecutive y-values.
First, let's calculate the differences between the y-values:
- The difference between the y-values from x = 0 to x = 1 is 6.8 - 1.7 = 5.1.
- The difference between the y-values from x = 1 to x = 2 is 27.2 - 6.8 = 20.4.
- The difference between the y-values from x = 2 to x = 3 is 108.8 - 27.2 = 81.6.
- The difference between the y-values from x = 3 to x = 4 is 435.2 - 108.8 = 326.4.
The differences between consecutive y-values are not constant. This suggests that a linear function (where the differences are constant) may not accurately model the data.
Next, let's calculate the ratios between the y-values:
- The ratio between the y-values from x = 0 to x = 1 is 6.8 / 1.7 = 4.
- The ratio between the y-values from x = 1 to x = 2 is 27.2 / 6.8 = 4.
- The ratio between the y-values from x = 2 to x = 3 is 108.8 / 27.2 = 4.
- The ratio between the y-values from x = 3 to x = 4 is 435.2 / 108.8 ≈ 4.
The ratios between consecutive y-values are constant (approximately 4). This suggests that an exponential function (where the ratios are constant) may accurately model the data.
Thus, based on the calculations, an exponential function is likely the best model for the given data in the table.
So what did you test for ?
Did you notice that the x values increase by 1 unit
Is the difference between consecutive y values a constant? <---- if so, arithmetic or linear
is the common ratio between consecutive y values a constant? <----- if so, geometric or exponentioal
are the second difference between y values constant? <---- if so, then quadratic