Final answer:
To find the exponential function that goes through the given points, we substitute the coordinates into the equation y = ab^x and solve for a and b.
Step-by-step explanation:
To write an exponential function in the form y = ab^x that goes through the points (0, 20) and (2, 720), we need to find the values of a and b. First, we plug in the coordinates of the first point into the equation to get 20 = ab^0. Since any number raised to the power of 0 is 1, we can simplify the equation to 20 = a. Next, we plug in the coordinates of the second point and solve for b: 720 = ab^2. Substituting a = 20, we get 720 = 20b^2. Dividing both sides by 20, we get 36 = b^2. Taking the square root of both sides, we find b = 6. Therefore, the exponential function is y = 20 * 6^x.