Step 1 :Input the given data into your graphing calculator. The x-values are the years (subtract 1980 from each year to make calculations easier), and the y-values are the percent of paper recycled.
Step 2 :Use the calculator's regression function to fit the data to an exponential function. This function is often labeled as 'ExpReg' or something similar on most graphing calculators.
Step 3 :The calculator will output the values of \(a\) and \(b\) for the function \(y=a b^{x}\). These are the values you're looking for.
Step 4 :To find \(R(x)\) in 2007, simply plug in \(x=2007-1980=27\) into the function \(y=a b^{x}\) and calculate the result.
Step 5 :Remember to round your final answers to six decimal places as needed.