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Determine whether each of the following tables of values could correspond to a linear function, an exponential function, or neither. For each table of values that could correspond to a linear or an exponential function, find a formula for the function.

If the function is neither linear nor exponential, enter NA.


(a)


The table of values corresponds to

neither a linear function nor an exponential functiona linear functionan exponential function

.

(b)


The table of values corresponds to

neither a linear function nor an exponential functiona linear functionan exponential function

.

(c)


The table of values corresponds to

an exponential functionneither a linear function nor an exponential functiona linear function

.

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Explanation / Answer

Notice x is changing linearly by 1
And y is changing by 10.5 - 9.2, i.e 1.3
Then changing by 5
Then changing by 15.1

Certainly exponential.

y = A*b^x

Using (0 , 9.2) :
y = 9.2*(b)^x

Using (1 , 10.5) :
10.5 = 9.2 * b^1
b = 105/92

So, exponential is :

y = 9.2 * (105/92)^x ----> ANSWER

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b)
(-1 , 56.1)
(0 , 50.49)
(1 , 45.441)
(2 , 40.8969)

x decreasing linearly by 1
y does not decrease linearly

This is exponential again

y = 50.49 * b^x

Using (1 , 45.441) :
45.441 = 50.49 * b^(1)
b = 0.9

So, we have
50.49(0.9)^x

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c)
(0 , 54)
(2 , 49)
(4 , 44)
(6 , 39)

x increases linearly by 2
And y decreaseslinearly by 5

So, we have linear function here

y = mx + b
Using (0 , 54)m we have

y = mx + 54

Clearly slope = (y2 - y1) / (x2 - x1)
m = (49 - 54) / (2 - 0)
m = -5/2
m = -2.5

So, y = -2.5x + 54

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