Answer: Let's assume that the exponential function we are looking for is of the form:
y = ab^x
where a and b are constants that we need to find.
Using the two points given, we can set up a system of equations:
48 = ab^2
192 = ab^3
We can divide the second equation by the first equation to eliminate a:
(192/48) = (ab^3)/(ab^2)
4 = b
Now we can substitute b = 4 into one of the original equations to solve for a:
48 = a(4)^2
48 = 16a
a = 3
Therefore, the exponential function that passes through the points (2, 48) and (3, 192) is:
y = 3(4)^x