MHB Finding the Equation of a Function.

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The discussion focuses on finding the equation of a function represented by the points (0, 2), (1, 4), (2, 10), and (3, 28). Participants suggest trying a cubic equation of the form ax^3 + bx^2 + cx + d to derive coefficients a, b, c, and d. A recurrence relation is also proposed, where a_{n+1} = a_n + 2 * 3^{n-1} with a_0 = 2. Additionally, subtracting 1 from the function values may reveal a recognizable sequence. The goal remains to accurately represent the function mathematically.
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The following points are part of a table of values for a function.
(0, 2), (1, 4), (2, 10), (3, 28)
Represent this function as:
a) equation
 
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Try a cubic of the form $ax^3+bx^2+cx+d$ substitute your values to solve for $a,b,c,d$ , what do you get?
 
Hello, vivalajuicy!

The following points are part of a table of values for a function:
. . (0,2), (1,4), (2,10), (3,28)
Represent this function as: (a) equation
I don't have the equation yet, but I have a recurrence.

. . a_{n+1} \;=\;a_n + 2\!\cdot\!3^{n-1},\;\;\;a_0 = 2
 
vivalajuicy said:
The following points are part of a table of values for a function.
(0, 2), (1, 4), (2, 10), (3, 28)
Represent this function as:
a) equation
The values of the function are 2, 4, 10, 28. If you subtract 1 from each of those, it may give you a sequence that looks familiar.
 

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