Lesson 7D: Solving Problems Using Logarithmic Functions

Jacob Bernoulli was the first mathematician to discover a practical application involving the mathematical constant e. He was investigating the effects of compound interest when the number of compounding periods was increased. He observed that, when the number of compounding periods became extremely large, the best function to model this type of growth had a base of e.

The value e makes sense as a model for natural growth. For example, if a population of rabbits grows at an average rate of 8% per year, this does not mean that eight rabbits are born at the end of every year (compounded annually) or that four rabbits are born at the end of every six months (compounded semi-annually). Populations of rabbits and other living things grow naturally and continuously. In other words, they have infinite compounding.

Logarithmic functions with base e model this continuous type of growth. This is part of why the natural logarithm is used in calculator and computer programs.

In this Training Camp, you will study the natural logarithm and its use as a logarithmic regression model.

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

	graph data and determine the logarithmic function that best fits the data
	interpret the graph of a logarithmic function that models a situation, and explain your reasoning
	use technology to solve a problem that involves data best modelled by a logarithmic function