Write an exponential function 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

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:

    (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:

   ...

The given two points of the exponential function are (2,24) and (3,144).

To determine the exponential function

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:

    (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:

    (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.

Plug-in this to EQ2.

And, solve for b.

Now that the value of b is known, plug-in this to EQ1.

And, solve for a.

Then, plug-in the values of a and b to

So this becomes

Therefore, the exponential function that passes the given two points is .