`(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
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.
Plug-in this to EQ2.
`144 = 24/b^2 * b^3`
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 `y=2/3*6^x` .