Which kind of function best models the data in the table? Use differences or ratios.
x y
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2
A.linear
B.quadratic
C.exponential
D.none of the above
I think it is C...?
Its c
To determine which kind of function best models the given data, we can examine the differences or ratios between consecutive values of y.
Let's start by calculating the differences between consecutive values of y:
1st difference: 6.8 - 1.7 = 5.1
2nd difference: 27.2 - 6.8 = 20.4
3rd difference: 108.8 - 27.2 = 81.6
4th difference: 435.2 - 108.8 = 326.4
Based on the first differences, we observe a pattern:
5.1, 20.4, 81.6, 326.4
The second differences are also consistent:
20.4, 61.2, 244.8
From this analysis, we can see that the differences increase by a factor of approximately 4 each time. This suggests that an exponential function may be the best fit for the data.
Hence, your answer of C. exponential seems correct.
looks like
y = 1.7(4)^x
sorry about repeat
yes, 1.7 * 4^x
first difference table
6.8 - 1.7 = 5.1
27.2 - 6.8 = 20.4
108.8 - 27.2 = 81.6
435.2 - 108.8 = 326.4
so not linear
second differences
20.4 - 5.1 = 15.3
81.6 - 20.4 = 61.2
326.4 - 81.6 = 244.8
so not quadratic
try ratios
6.8/1.7 = 4
27.2/6.8 = 4
ah hah ! constant ratio of 4