The derivatives of exponential functions show a very interesting pattern. Your task in this activity is to find the pattern.

1. Start with the exponential function defined by the equation y = 2^x.
1. Your first task is to create an In-Out table like the one shown here.
   
   

   x-value	y-value	Derivative

   
   
   Use these two steps to get a row of the table.
   
   
   • Pick a whole-number valuse for x and find the y-value that goes with it.
     
     
   • Get a good approximation for the derivative of the function at the point on the graph of the function y = 2^x that is represented by your x- and y-values.
     
     
   Go through these two steps for several points to get several rows for the table.
   
   
2. Once you have several rows for your table, study the data and write an equation expressing the derivative in terms of the y-value. (If nececcary, develop more rows of the table.)
2. Repeat the process described in Question 1, but this time use the function whose equation is y = 10^x
   
   .
3. Pick a thrid exponential function and go through the process from Question 1 for that function.