MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

18
MAT 142 Lecture Video Series

description

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

Transcript of MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Page 1: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

MAT 142Lecture Video

Series

Page 2: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Exponential Functions and Their Inverses

Page 3: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

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

graph.

Page 4: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Functions

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

y f red(x) 3x 2

Page 5: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Evaluate.

y f red(x) 3x 2

y tax(d) .18d

y g(x) 3x 2 2x

f red(4)

tax(50)

g()

Page 6: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

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

Page 7: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Graph each of the following functions.

h(t) e13t

g(t) e4t

f (t) e1t

Page 8: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

h(t) e13t

g(t) e4t

f (t) e1t

red

green

blue

Page 9: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Graph each of the following functions.

g(t) e 4t

f (t) e4t

Page 10: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

g(t) e 4t

f (t) e4t

green

blue

Page 11: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

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

Page 12: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Graph each of the following functions.

h(t) 14

e3t

g(t) 4e3t

f (t) e3t

Page 13: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

h(t) 14

e3t

g(t) 4e3t

f (t) e3t

red

blue

green

Page 14: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Inverse of the Natural Exponential Function

t 1k

ln ya

y aekt

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

Page 15: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Write the inverse of the exponential function

g(t) 4e3t

Page 16: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

Write the inverse of the exponential function

h(t) 14

e 7t

Page 17: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

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?

Page 18: MAT 142 Lecture Video Series. Exponential Functions and Their Inverses.

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