Finding the Equation of a Function.

[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

 

[pickslides]

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?

 

[soroban]

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.

. . $$a_{n+1} \;=\;a_n + 2\!\cdot\!3^{n-1},\;\;\;a_0 = 2$$

 

[Opalg]

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.