Can anyone explain the steps? The formula of an exponential function from two points. Reddit algebra

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#math #algebra #mathbasics

[easternns]

So much math...so little time. Thank you for posting these videos. As a science and math tutor I find these so very helpful in brushing up on my own math skills.

[PowerShellWizard]

At 5:37 i dont get why the base mist be positive. I would think there wouod be two satisfactory equations, one for the positive base and one for the negative base. If the excercise is to find "a" matching exponential function then we should allow for a negative base

[okaro]

2:27 With the precision given b=2 is a good enough answer. log2 (4/1.3) = 1.621488.

[reubenmenezes]

Thanks a lot for this video! I know this may be a weird question, but what watch are you wearing? Love it haha

[Frederic]

For the first one, b has to be considered as being exactly 2, because the coordinate values are approximate.

[emmeeemm]

The common intuition that "2 points define a line" is cool enough and all, but this demonstration that 2 points also seem to define an exponential curve is wild.

As I compose this comment, I have a feeling that it might actually take 3 points to uniquely define an exponential curve in R2, just to clear up any ambiguous roots. If a third point is necessary, then a third parameter might be needed for a more "complete" equation, and after playing with parameters in Desmos for a few minutes, I think that third parameter is a vertical translation. It looks to me like we need "y=a*b^x + k" to fully describe all exponential curves in R2. Yeah, without a vertical translation term, the horizontal asymptote of the curve is always y=0, but if we translate up or down, it can be y=k.

[dannyyeung]

It is similar to a type of HKDSE question

[major__kong]

You can take the log of both sides.

log(y) = log(a) + log(b)*x

Now you have a linear system in x. Let c = log(a) and d = log(b)

log(y) = c + d*x

Solve for c and d using standard system of equations techniques. Then a = 10^c and b = 10^d.