Explanation:
Since we are looking for an exponential equation in the form y = a·b^x, where b is the base of the exponential function, we can use the two given points to set up a system of equations and solve for a and b.
Using the point (3, 2), we have:
2 = a·b^3
Using the point (6, 16), we have:
16 = a·b^6
Dividing the second equation by the first equation, we get:
16/2 = (a·b^6) / (a·b^3)
8 = b^3
Taking the cube root of both sides, we get:
b = 2
Substituting this value of b into either of the two equations, we can solve for a. Using the first equation, we have:
2 = a·2^3
2 = 8a
a = 1/4
Therefore, the exponential equation that passes through the points (3, 2) and (6, 16) and has an asymptote of y=0 is:
y = (1/4)·2^x
or
y = 0.25·2^x