1.5 Exponential Functions Math 150 Introduction to Calculus.

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Presentation transcript:

1.5 Exponential Functions Math 150 Introduction to Calculus

An Exponential Function  As an example to begin with, consider the function f(t) = 2 t. Then f(1) = 2, f(2) = 2 2 = 4 and so on.  The number 2 is called the base of the function, and its exponent is variable.  Exponential functions show up in a variety of applications.

Population Growth  Population growth is one example  The rate of growth depends on the size of the population

Drug Concentrations  The amount of a drug in the bloodstream decreases naturally due to metabolic activity  Over time, the amount leaving the blood stream depends on the amount in the bloodstream

Exponential Functions

Linear vs. Exponential

Seeing Patterns in Data

…and the Solution

The number e  Yes, e is a number. It is a constant value like   e is a commonly used base for exponential functions, f(t) = e t  e is special because the function f(t) = e t has a rate of change that makes it useful in finance, science and mathematics

Families of Exponentials  In the graphs below, functions for exponential growth and exponential decay are plotted for different values of the base a  The graph of f(t) = e t is shown on the left