Question 138990
Below are two sets of data.  One of the sets describes a linear function and the other describes an exponential function.  Which is linear and which is exponential?  Explain how you know.  Find a formula for each function.  For this problem, it is not acceptable to use results from your graphing calculator.    

Table 1
x,	g(x)
-2,	0.4444
-1,	1.3333
0,	4
1,	12
2,	36
3,	108
4,	324
5,	972
6,	2916
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Looking at g(0) and g(1) you see there is a ratio of 12/4= 3
That ratio continues thruout the table.
So : Exponential with y = ab^x
Use (0.4) to find "a"; 4 = a^b^0; a = 4
So y = 4b^x
Use (1,12) to find "b"; 12 = 4b^1
b = 3
EQUATION:  g(x) = 4*3^x
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Table 2
x,	f(x)
  -2,	4
-1,	3.5
0,	3
1,	2.5
2,	2
3,	1.5
4,	1
5,	0.5
6,	0
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Look at f(1)/f(0)= 2.5/3 = (5/2/3) = 5/6
Look at f(2)/f(1) = 2/2.5 = 2/(5/2) = 4/5
No common ratio
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Look at the successive difference: it is -1/2.
Eq. form y = mx + b
Since f(0) = 3, b= 3
Since y decreases (1/2) when x increases 1, m= -1/2
EQUATION: y = (-1/2)x + 3
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