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Linear or Nonlinear? Find the next 2 values in the table. Can you find the rule? If not, why?

Linear or Nonlinear? Find the next 2 values in the table. Can you find the rule? If-example-1
User Sheodox
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1 Answer

3 votes

9514 1404 393

Answer:

linear

(x, y) = (36, 54), (68, 102)

Explanation:

We observe that y-values are proportional to x-values with a constant of proportionality of 1.5. This is a linear function.

"The next 2 values in the table" presumes we can find the rule for choosing x. For the answer above, we have observed that first differences in x-values increase by powers of 2:

8-6 = 2

12 -8 = 4

20 -12 = 8

So we have chosen the next two x-values to be 16 and 32 more than the one before:

next x = 20 +16 = 36

x after that = 36 +32 = 68

That is, the rule for x is ...

xn = 4 + 2^n

and the rule for y is ...

y = 1.5x . . . a linear function

User Edwin Liu
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4.8k points