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
NO
quadratic?
7.8 / 1.3 = 6
46.8 / 7.8 = 6
every one is 6 times the previous
https://www.basic-mathematics.com/geometric-sequence.html
https://socratic.org/algebra/exponents-and-exponential-functions/geometric-sequences-and-exponential-functions
To determine which kind of function best models the data in the table, we can use differences or ratios.
First, let's calculate the differences between consecutive y-values:
Difference between the 1st and 2nd y-value: 7.8 - 1.3 = 6.5
Difference between the 2nd and 3rd y-value: 46.8 - 7.8 = 39
Difference between the 3rd and 4th y-value: 280.8 - 46.8 = 234
Difference between the 4th and 5th y-value: 1684.8 - 280.8 = 1404
Looking at the differences, notice that they are not constant. In a linear function, the differences between consecutive y-values would be constant. Therefore, we can conclude that the data does not fit a linear function.
Next, let's calculate the ratios between consecutive y-values:
Ratio between the 1st and 2nd y-value: 7.8 / 1.3 ≈ 6
Ratio between the 2nd and 3rd y-value: 46.8 / 7.8 ≈ 6
Ratio between the 3rd and 4th y-value: 280.8 / 46.8 ≈ 6
Ratio between the 4th and 5th y-value: 1684.8 / 280.8 ≈ 6
Looking at the ratios, notice that they are approximately constant. In an exponential function, the ratios between consecutive y-values would be constant. Therefore, we can conclude that the data fits an exponential function.
Based on this analysis, the best answer is c. exponential.