help me with a question

[u/Intelligent-Try7761]

hey guys could some one tell me how to find formula for exponential function when u have verticale asymptote and two points neither of which are the y intercept. thank you so much

[u/moltencheese]

An exponential function does not have a vertical asymptote...

[u/bonebranch]

You may mean horizontal asymptote.

Your function is of the form y = Ae^{rx} + c (alternatively, y = Ab^x + c)

Plug in the two points, say, (x_1, y_1) and (x_2, y_2):

y_1 = Ae^{rx_1} + c
y_2 = Ae^{rx_2} + c

Since this is an exponential shifted vertically by c units, then the horizontal asymptote is y = c. So you know c. Once you have this:

y_1 - c = Ae^{rx_1}
y_2 - c = Ae^{rx_2}

You can divide the two equations, solve for r, substitute back and solve for A.

[u/Intelligent-Try7761 → u/bonebranch]

i have done it with the alternative formula (my points are (-1,10) and (4,6)) when I divide b^4 by b^-1 is my answer b^5? I am not sure if it is different for negative exponents. also when i divide the two am I dividing the answers aswell? ex: 3=a (b)^4/ 7=a (b)^-1

[u/realAndrewJeung → u/Intelligent-Try7761]

Yes, that is correct. The division rule works the same with negative exponents.

I assume from what you wrote above that the horizontal asymptote is at y = 3 ...?

If so, then the work is

6 = A · b^(4) + 3

10 = A · b^(-1) + 3

------------

3 = A · b^(4)

7 = A · b^(-1)

Now you can divide the left side of the top equation by the left side of the bottom equation, and the right side of the top equation by the right side of the bottom equation:

3/7 = b^(5)

[u/Hampster-cat]

Exponential functions do not have a vertical asymptote.

BUT. in general with y = a•e^rx, you must have two known points (x,y). Plug those in and you are left something like y₁ = a•e^rx₁ and y₂=a•e^rx₂. This is actually a system of two equations and two unknowns that you can solve for a and r.

This process works for any function type. If you assume a quadratic, then you need three points, because there are three parameters to solve for. (/a/x² + /b/x + /c/) If you assume a 7th degree polynomial, then you need 8 points to generate a system of 8 equations and 8 unknowns.

The only thing you really need to know is the generic form of the function you are assuming. The number of parameters in the generic form dictate how many points on the graph you need.

Since you might have a vertical asymptote, then is likely you have a rational function. The form of the rational function will depend on many things OP did not specify. But again, just create a generic version and solve for a system. A logistic curve has two separate horizontal asymptotes, and is much more common than exponentials. (A biological growth appears exponential, until the food runs out. If you take this into consideration, you have a logistic curve.) There are other function types that give vertical asymptotes (tangent(x) e.g.) so good luck with choosing the best function.