I have two points (x2,y2) and (x3,y3) that represent points in an exponential decay curve of discounted cash flows (x2 is less than x3):
My question is: What is the decay curve equation for the decay function that passes through two points and the y-axis at the maximum value of y, where x1=0 and y1=Maximum Possible?
First you have to evaluate the lower bound of your curve. Let denote it as $L$.
The function for exponential decay is $y=A\cdot e^{-bx}+L$
You have the two points $(x_2/y_2)$ and $(x_3/y_3)$. They can be inserted into the function:
$y_2=A\cdot e^{-bx_2}+L \quad (1)$
$y_3=A\cdot e^{-bx_3}+L \quad (2)$
Dividing (1) by (2).
$\frac{y_2-L}{y_3-L}=e^{b(x_3-x_2)}$
Taking logs
$log\left(\frac{y_2-L}{y_3-L} \right)=b(x_3-x_2)$
$b=\large{\frac{log\left(\frac{y_2-L}{y_3-L} \right)}{x_3-x_2}}$
Now you can use the value of $b$ to calculate $A$. Just insert the value of $b$ in one of the equation (1) or (2) and solve for $A$. $A$ is the y-intercept. This is the y-value of the point $(0/y_1)$.