1. Economics 214 Lecture 6

2. Polynomial Functions

3. The degree of the polynomial is the value taken by the highest exponent. A linear function is polynomial of degree 1. A polynomial of degree 2 is called a quadratic function. A polynomial of degree 3 is called a cubic function.

4. Roots of Polynomial Function

5. 3 cases for roots of quadratic function b 2 -4ac>0, two distinct roots. b 2 -4ac=0, two equal roots b 2 -4ac<0, two complex roots

6. Quadratic example

7. Plot of our Quadratic function

8. Exponential Functions The argument of an exponential function appears as an exponent. Y=f(x)=kb x k is a constant and b, called the base, is a positive number. f(0)=kb 0 =k

9. Exponential Functions

10. Figure 2.16 Some Exponential Functions

11. Exponential functions with k<0

12. Regional Growth in the U.S.

13. New England Income

14. Growth Formula

15. New England Personal Income Annual Growth Rate = 4% Our bar Chart is approximately a step function. We assume growth doesn’t occur until end of the year.

16. Step Function 19901990 199019911992199319941995 Income Year

17. Income Growth We have depicted the growth of income over time as a step function. It is usually more natural to think of continuous growth, which would be reflected in a smooth evolution over time of variables like income and population.

18. Multiple Compounding in one Period

19. Effect of Number of compounds at 4%

20. Effect of Number of Compounds at 4%

21. Figure 3.2 Compounding at Different Frequencies