Lesson 6C: Solving Problems Using Exponential Functions

Louis Pasteur was a French chemist and biologist who, in 1854, was appointed professor of chemistry at the University of Lille. Part of his responsibility was to find solutions to practical problems of local industries, particularly the manufacture of alcoholic drinks. Pasteur was able to demonstrate that organisms such as bacteria were responsible for souring wine and beer. Later, he extended his studies to prove that the souring of milk was similar. He showed that bacteria could be removed by boiling and then cooling the liquid. We know this process as pasteurization.

Considered a staple by many, milk is now pasteurized in modern processing plants to eliminate disease-causing bacteria and reduce the number of spoilage micro-organisms. During pasteurization, the milk is passed through heated tubing so its temperature rises to 71°C for fifteen seconds. Not all spoilage micro-organisms are eliminated, but a sufficient number are, thus greatly increasing the shelf life of milk.

One measure of how the number of micro-organisms can be reduced by heating is the decimal reduction time, D. This is the time required to reduce the quantity of micro-organisms by a factor of ten. The function that relates the micro-organism population to D is . This function is a real life application of the exponential function y = abx.

In this Training Camp, you will use exponential functions to model various real life situations and solve related problems.

By the end of this lesson, you should be able to

graph data and determine the exponential function that best fits the data
use technology to solve a problem that involves data best modelled by an exponential function
solve problems that involve the application of exponential equations to loans, mortgages and investments