Question
Determine if the following tables represent linear, quadratic, exponential, or neither and explain why. in 1 sentence
A.
x|y
-2|7
-1|4
0|1
1|-2
2|-5
B.
x|y
-1|1.5
0|3
1|6
2|12
C.
x|y
-1|-9
1|9
3|27
5|45
D.
x|y
-2|6
-1|3
0|2
1|3
2|6
E.
Volleyball Tournament
Round|Teams Left
1|16
2|8
3|4
4|2
F.
x|f\left(x\right)=2\left(3\right)^{x}
1|6
2|18
3|54
4|162
A.
x|y
-2|7
-1|4
0|1
1|-2
2|-5
B.
x|y
-1|1.5
0|3
1|6
2|12
C.
x|y
-1|-9
1|9
3|27
5|45
D.
x|y
-2|6
-1|3
0|2
1|3
2|6
E.
Volleyball Tournament
Round|Teams Left
1|16
2|8
3|4
4|2
F.
x|f\left(x\right)=2\left(3\right)^{x}
1|6
2|18
3|54
4|162
Answers
GPT-4o mini
A. The table represents a linear relationship because the differences between consecutive y-values are constant (-3).
B. The table represents an exponential relationship because the ratios of consecutive y-values are constant (1.5, 2, 2).
C. The table represents a quadratic relationship because the second differences of the y-values are constant (18, 18).
D. The table represents neither a linear, quadratic, nor exponential relationship because it does not maintain a consistent rate of change, nor does it exhibit a pattern consistent with the other types.
E. The table represents an exponential relationship because the number of teams left halves in each subsequent round.
F. The table represents an exponential relationship with base 3, as it follows the function f(x) = 2(3)^x with y-values consistently increasing by a factor of 3.
B. The table represents an exponential relationship because the ratios of consecutive y-values are constant (1.5, 2, 2).
C. The table represents a quadratic relationship because the second differences of the y-values are constant (18, 18).
D. The table represents neither a linear, quadratic, nor exponential relationship because it does not maintain a consistent rate of change, nor does it exhibit a pattern consistent with the other types.
E. The table represents an exponential relationship because the number of teams left halves in each subsequent round.
F. The table represents an exponential relationship with base 3, as it follows the function f(x) = 2(3)^x with y-values consistently increasing by a factor of 3.