Answer:
A: Exponential
B: Quadratic
C: Linear
Step-by-step explanation:
Solution:-
- We will closely inspect each Table and find the difference between each "Y" value at every unit increase in "x" value:
Table A:
X Y ΔY/ΔX
1 5 xxxxxx Exponential because [ ΔY/ΔX ]
2 11 11 - 5 = 6 increases at the fastest rate out of all
3 29 29 - 11 = 18 functions.
4 83 83 - 29 = 54
5 245 254 - 83 = 171
6 731 731 - 254 = 477
Table B:
X Y ΔY/ΔX Δ^2Y/ΔX^2
0 5 xxxxxx xxx Quadratic because
1 7 7 - 5 = 2 xxx Δ^2Y/ΔX^2 is a constant
2 13 13 - 7 = 6 6-2 = 4 for all quadratic functions
3 23 23 - 13 = 10 10-6 = 4
4 37 37 - 23 = 14 14-10 = 4
5 55 55 - 37 = 18 18-14 = 4
Table C:
X Y ΔY/ΔX
3 20 xxxxxx Linear because
6 18 2 / 3 ΔY/ΔX is a constant
9 16 2 / 3 for all linear functions
15 12 2 / 3
27 4 8/12 = 2/3
39 -4 8/12 = 2/3
