Find the equation of a non-linear relation given 2 points

manpreet Best Answer 2 years ago

So I ask my question, let me just begin by stating that I'm in grade 9, and have decided to start learning calculus to aid me in the development of an undisclosed project that I am working on.

Now, I am very new to calculus, and my terminology may be wrong so please correct me if I make any mistakes. So I have the data set:

| Binary Position |  Decimal Value  |
|:---------------:|:---------------:|
|        0        |        1        |
|        1        |        2        |
|        2        |        4        |
|        3        |        8        |
|        4        |       16        |
|        5        |       32        |
|        6        |       64        |
|        7        |      128        |
|        8        |      256        |
|        9        |      512        |

(Which by the way is the binary to decimal conversion table for each position pertaining a value of 1in the binary string). I need to find the relation between the binary position and decimal value or the independent X and the dependent Y values so that I can dynamically calculate the decimal value for a given position in the binary string, say for example (x=15,y=32768)(x=15,y=32768) which I could only calculate by extending the table using the relation between the individual collums. I know that the relation between the X values is +1 and the relation between the Y values is x2 but how would I go about finding the equation of the curve? I know that the traditional method of finding the equation of a line is

1) Find the slope using ΔyΔx=yn+1−ynxn+1−xnΔyΔx=yn+1−ynxn+1−xn

2) Substitute the product of ΔyΔxΔyΔx into "mm" of y=mx+by=mx+b

3) Solve for "bb" (the y-intercept) by substituting in a point into y=mx+by=mx+b and solving as b=mx+yb=mx+y

4) Reconstruct the equation with the slope and y-intercept in "

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