Economists use nonlinear functions to analyze the behavior of unit costs and productivity, as well as the relationship between the price of an item and the quantity demanded. The financial world could not operate without the nonlinear functions that represent the compounded growth of investments. Each of these functions has a unique and standard shape that you may find yourself recognizing easily after you complete this section of the course.
Each nonlinear equation contains an exponent that causes the function to form a curve when graphed. To manipulate or solve nonlinear functions, an understanding of exponents, roots, and logarithms is important. Mathematical principles guide the manipulation of exponents, roots, and logarithms.
Using calculus to find the derivatives of nonlinear equations is also useful to businesses attempting to solve optimization problems. Average cost and productivity functions are good examples of nonlinear functions. Operations managers are interested in finding the minimum and maximum pointsor extremaon these functions and targeting their production accordingly.
When you have completed the Precalculus section, you should be able to
- solve business problems using exponents, roots, and logarithms
- identify three common nonlinear functions used in business
- determine the slope of nonlinear functions, as well as the maximum and minimum points of these functions