United States Patents

In this project we are going to compare the difference between using a quadratic function and an exponential function to model the growth in the number of patents issued in the United States. The table below gives the first U.S. patent number by year. You will need to determine the first U.S. patent number for last year and add this point to your data set before making your scatterplot. To access this information go here. Let x = 0 for the year 1856 and have a statistical package or a graphing calculator make a scatterplot with the number of years since 1856 being the independent variable and the first patent number issued x years after 1856 being the dependent variable. Have a statistical package or a graphing calculator fit a quadratic equation to this data set. Using this quadratic equation, predict the first patent number that will be issued for next year. Using the quadratic equation, predict the first patent number that was issued in 1836.

First U.S. patent number in each calendar year

With a statistical package or a graphing calculator fit an equation of the form ln y =. . . . Rewrite this equation using properties of exponents so it is of the form y = . . . . Use this equation to predict the first patent number that will be issued for next year. Using this exponential equation, predict the first patent number that was issued in 1836. (The first patent number was actually issued in 1836.)

Compare your quadratic predictions with your exponential predictions and the actual patent numbers that have been issued. Which equation do you think gives the better predictions, the quadratic or exponential? Explain.