To write an exponential function in the form y = ab^x that goes through the points (0,11) and (2,396), we can use the fact that the exponential function is defined as y = ab^x, where a is the initial value and b is the growth factor.
First, we can find the growth factor by using the following equation: b = y2/y1.
In this case: b = 396/11 = 36
Next, we can use the point (0,11) and the growth factor to find the value of a.
Since we know that y = ab^x, we can substitute the point (0,11) and the growth factor into the equation:
11 = a(36)^0
a = 11
So, the exponential function that goes through the points (0,11) and (2,396) is: y = 11 * 36^x
It is important to note that the above function will pass through the points (0,11) and (2,396) but it may not pass through any other points. It is also a good practice to check the function by substituting the point (0,11) and (2,396) to confirm it gives the correct output.