the definition of an exponential equaiton is an equation in the form:
y = ab^x
to find the actual equation, we will need values of a and b and we can use the coordinates given to help us with that
(1, 15): 15 = ab^1
ab = 15
(2, 45): ab^2 = 45
remember that whatever operation we do on one side of the equation, as long as we do it on the other side, the equality will be maintained (rule a). looking at the eqation ab^2 = 45, we can divide ab on the left side, and instead of dividing by ab on the right side, we can divide something equal to ab which will not violate rule a. that number is 15 because ab = 15 in our first equation!!! doing so yields
b = 45/15
so b = 3. now we have b, we can once again use the first equation to find that a = 5. therefore, our desired equation is:
y = 5*3^x
let me know if you have any questions!
