MAT 142 Lecture Video Series. Exponential Functions and Their Inverses

MAT 142Lecture Video

Series

Exponential Functions and Their Inverses

Objectives• Evaluate a function at a given value.• Match an exponential function to its

graph.

Functions

• x is the independent variable.•Y is the dependent variable.•fred is the name of the function.

y f red(x) 3x 2

Evaluate.

y f red(x) 3x 2

y tax(d) .18d

y g(x) 3x 2 2x

f red(4)

tax(50)

g()

Basic Natural Exponential Function

• a is the initial amount (f(0))•e is a number that is approximately 2.71828 (it is on your calculator)

y f (t) aekt

Graph each of the following functions.

h(t) e13t

g(t) e4t

f (t) e1t

h(t) e13t

g(t) e4t

f (t) e1t

red

green

blue

Graph each of the following functions.

g(t) e 4t

f (t) e4t

g(t) e 4t

f (t) e4t

green

blue

Basic Natural Exponential Function

• a is the initial amount (f(0))

• k > 0, function strictly increases

• k < 0, function strictly decreasing

y f (t) aekt

Graph each of the following functions.

h(t) 14

e3t

g(t) 4e3t

f (t) e3t

h(t) 14

e3t

g(t) 4e3t

f (t) e3t

red

blue

green

Inverse of the Natural Exponential Function

t 1k

ln ya

y aekt

Where a, k, and t come from the natural exponential function.

Write the inverse of the exponential function

g(t) 4e3t

Write the inverse of the exponential function

h(t) 14

e 7t

The number of bacteria in a culture is given by the function

where t in measured in hours.

n(t) 900e0.1t

How many bacteria will the culture contain in 5 hours?

Creator and Producer

Elizabeth Jones

for

The School of Mathematical and Statistical Sciences

atArizona State University

Videographer

Mike Jones

©2010 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University