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

[@easternns1]

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.

[@reubenmenezes1139]

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

[@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

[@MarieAnne.]

When dealing with a continuous real-valued function, then base must be positive, otherwise the function is undefined almost everywhere and discontinuous at all points where it is defined. The function y = −2 (−0.75)^x is defined for integer values of x and for some rational values of x. But even if you were only interested in integer values of x, we still get points that will not be located on the curve shown. Let's see what happens at x = 2, 3, 4 x = 2, y = −2 (−0.75)^2 = −1.125 x = 3, y = −2 (−0.75)^3 ≈ 0.844 > 0 x = 4, y = −2 (−0.75)^4 ≈ −0.633 Now if you look at the curve, the value of y is negative when x = 3, but with a negative base, the value of y becomes positive. So you might say let's make a positive instead. Well this will work for x = 3, but y will become negative at x = 2 and x = 4. The only way to get y negative at all instances of x is for b to be positive and a negative. This will also ensure that the function is defined and continuous for all real values of x.

[@Frederic7594]

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

[@bobh6728]

Since the y value is given as 4 and not 4.000 in a science class that would mean 4 ±.5. So your answer can’t have 5 significant digits when the given only has 1. But if these are exact numbers, then his 2.0004 is correct.

[@butterspread4104]

@@bobh6728 i did the same in physics at the start of this year lol

[@okaro6595]

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

[@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.

[@PowerShellWizard]

There is also an implicit assumption the function is a function and is continuous , which in reality there is no guarantee for whatsoever

[@Mrpatlolive804-z8r]

Thanks 😊😊

[@bugsfudd8295]

Nice almost forgot how to do those

[@dannyyeung8237]

It is similar to a type of HKDSE question

[@timothymcglynn1935]

Hi 👋

[@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.

[@yadav-raj258]

India view kon kon hai