(1,3) , (2,12) Write an exponential function y=ab^x whose graph passes through the given points.

The given two points of the exponential function are (1,3) and (2,12).
To determine the exponential function
y=ab^x
plug-in the given x and y values.
For the first point (1,3), plug-in x = 1 and y=3.
3=ab^1
3=ab        (Let this be EQ1.)
For the second point (2,12), plug-in x=2 and y=12.
12=ab^2     (Let this be EQ2.)
To solve the values of a and b, apply the substitution method of system of equations. To do so, isolate the a in EQ1.
3=ab
3/b= a
Plug-in this to EQ2.
12=ab^2
12=(3/b)b^2
And, solve for b.
12=3b
12/3=b
4=b
Plug-in this value of b to EQ1.
3=ab
3=a(4)
And, solve for a.
3/4=a
Then, plug-in the values of a and b to the exponential function
y=ab^x
So, this becomes:
y = 3/4*4^x
Therefore, the exponential function that passes the given two points is y=3/4*4^x .