Which kind of function best models the data in the table? Use differences or ratios.
x y
0 1.3
1 7.8
2 46.8
3 280.8
4 1684.8
a. linear **
b. quadratic
c. exponential
d. none of the above
could someone check my answer please
i meant to say quadratic **
To determine the type of function that best models the data in the table, we can examine the differences or ratios between consecutive y-values.
Let's start by finding the differences between consecutive y-values:
1.3 (7.8 - 1.3 = 6.5)
7.8 (46.8 - 7.8 = 39)
46.8 (280.8 - 46.8 = 234)
280.8 (1684.8 - 280.8 = 1404)
As you can see, the differences increase rapidly with each consecutive x-value, which suggests that a linear function does not adequately model the data.
Next, let's calculate the ratios between consecutive y-values:
1.3 (7.8 / 1.3 ≈ 6)
7.8 (46.8 / 7.8 ≈ 6)
46.8 (280.8 / 46.8 ≈ 6)
280.8 (1684.8 / 280.8 ≈ 6)
The ratios between the y-values are approximately the same, which indicates that an exponential function might be a good fit for the data.
Based on the differences and ratios, we can conclude that the data is best modeled by an exponential function. Therefore, the correct answer is c. exponential.
Remember, it's always recommended to verify your answer with a mathematical model or graphing the data to confirm the best-fit function.