Example
Let's find an equation of the exponential curve $y = Ab^x$ through $(1, 10.4)$ and $(3, 41.6)$.
Step 1 Substitute the coordinates of the given points in the equation $y = Ab^x$:
$10.4 = Ab^1$ \t
\\ $41.6 = Ab^3.\qquad$ \t
Step 2 Divide the second equation by the first to eliminate the constant $A$ ad solve for $b$:
$\displaystyle \frac{41.6}{10.4} = \frac{Ab^3}{Ab}$ = $b^2$
\\ $\displaystyle b^2 = \frac{41.6}{10.4} = 4$
\\ $\displaystyle b = 4^{1/2} = 2$ \t
Step 3 Substitute for $b$ in either equation to obtain $A$:
$10.4 = A(2^1) = 2A \qquad$ \t
\\ $\displaystyle A = \frac{10.4}{2} = 5.2$
#[Thus we have $A = 5,2$ and $b = 2$, so that our desired equation is][Por lo tanto, tenemos $A = 5.2$ y $b = 2$, de modo que nuestra ecuación deseada es]#
$y = 5.2(2^x). \qquad$ \t