(2,24) , (3,144) Write an exponential function y=ab^x whose graph passes through the given points.

The given two points of the exponential function are (2,24) and (3,144).
To determine the exponential function
y=ab^x
plug-in the given x and y values.
For the first point (2,24), the values of x and y are x=2, y=24. Plugging them, the exponential function becomes:
24=ab^2     (Let this be EQ1.)
For the second point (3,144), the values of x and y are x=3 and y=144. Plugging them, the function becomes:
144=ab^3     (Let this be EQ2.)
To solve for the values of a and b, apply substitution method of system of equations. To do so, isolate the a in EQ1.
24=ab^2
24/b^2=a
Plug-in this to EQ2.
144=ab^3
144 = 24/b^2 * b^3
And, solve for b.
144=24b
144/24=b
6=b
Now that the value of b is known, plug-in this to EQ1.
24=ab^2
24=a*6^2
And, solve for a.
24=36a
24/36=a
2/3=a
Then, plug-in the values of a and b to
y=ab^x
So this becomes
y=2/3*6^x
Therefore, the exponential function that passes the given two points is y=2/3*6^x .