Question 992730
Your model in general {{{y=ab^x}}} is useful also for the logarithms of its left and right side
members.
Choose either base 10 or e.  Here will be using base 10.


{{{log(10,y)=log(10,(ab^x))}}}
{{{log(10,y)=log(10,a)+x*log(10,b)}}}
{{{highlight_green(log(10,y)=x*log(10,b)+log(10,a))}}}


You now want to adjust your given points to use {{{log(10,y)}}} instead of the y coordinates as given
because that is how the equation has been treated.  Your points to use in the green-outlined equation
must now be  (-2, log(10,1)) and  (2, log(10,5)).
Those points, if decimal form will help,  (-2,0) and  (2,0.6990).
-
Again, these points are for the LINEAR equation outlined in green - NOT for the original model
of {{{y=ab^x}}}.


Now you have the two points, treated for their logarithms of y, and you can find the
vertical axis intercept which is {{{log(10,a)}}} and the slope which is {{{log(10,b)}}}.
That allows you to find a and b.