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I've been working at solving this equation all night and I keep hitting dead-ends. Given the curve can be defined as $y = ab^x + c$ and the points $(-1, 0)$, $(0, 0.01)$, $(0.9, 0.5)$, and ($1, 1)$ exist on it, how do I find constants $a$, $b$ and $c$?

Aeren Sage
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1 Answers1

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You could solve this with only $3$ coordinates.

Plugging in the coordinates:

$$0=ab^{-1}+c \implies 0=\dfrac ab+c\tag1$$

$$0.01=ab^0+c \implies0.01=a+c\tag2$$

$$0.5=ab^{0.9}+c\tag3$$

$$1=ab^1+c \implies 1=ab+c \tag4$$

There are $4$ equations, $3$ unknowns. Out of those $4$ equations, focus on the $3$ easiest ones to solve (IMO $(1), (2)$, and $(4)$)

Can you solve the $4$ equations, or do you need further hints?

  • Sorry, I made a mistake when typing the coordinate pairs - I'll correct it. – Aeren Sage Mar 13 '18 at 00:43
  • @AerenSage Now? –  Mar 13 '18 at 00:52
  • Thank you, let me try quick – Aeren Sage Mar 13 '18 at 00:53
  • And @AerenSage, please check if your equation works if you plug in the $3$rd coordinate. If it doesn't, that could mean that either you are doing it wrong, or one of the points you mentioned do not belong on the equation at all. Please tell me your solution at the end. –  Mar 13 '18 at 00:54
  • I've found that a:0.01010 and b:99 for the equations that you suggested - given this a and b value, c:0 (rounded, though, to the nearest integer); c is inaccurate when taken at anything deeper than the closest integer which is 0. But for my purposes, the nearest integer will do.

    Thank you very much for your help.

     – Aeren Sage Mar 13 '18 at 01:14
  • P.S. If you find a more precise answer than I have would you please share with me how you got it.:) – Aeren Sage Mar 13 '18 at 01:20