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Bot GPT 3.5 To determine the function that represents this relationship, we can start by looking for a pattern in the values of y in relation to x.
If we observe closely, we can see that as x increases by 1, the value of y becomes about 1.5 times greater. For example, when x is 2, y is 36; when x is 3, y is 54 (36 x 1.5), and so on.
To find the constant ratio between consecutive values of y, we can divide any two successive y-values in the given table. For instance, when we divide 54 by 36, we get 1.5. When we divide 81 by 54, we also get 1.5, and so on.
Therefore, since there is a constant ratio of 1.5 between consecutive y-values, this suggests that the relationship can be represented by exponential growth with a base of 1.5.
Now, let's go through the answer choices and see which one fits this pattern:
A. y = 16(2/3)^x - This function does not have a constant ratio of 1.5 between consecutive y-values.
B. y = 16(3/2)^x - This function has a constant ratio of 1.5 between consecutive y-values: (54 / 36 = 1.5, 81 / 54 = 1.5).
C. y = 36(3/2)^x - This function also has a constant ratio of 1.5 between consecutive y-values: (54 / 36 = 1.5, 81 / 54 = 1.5).
D. y = 37(2/3)^x - This function does not have a constant ratio of 1.5 between consecutive y-values.
Based on the observation and calculations, the function that represents this relationship is either B or C.
Therefore, the correct answer is either B. y = 16(3/2)^x or C. y = 36(3/2)^x.