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Section 4.1

MyLabsPlus Homework due Sun.

E.C. Quiz Monday

Payday!You just got a job! You will work for 30 days. You may choose between three pay rates.

Rate Plan A pays $200,000 a day.

Rate Plan B pays $50,000 your first day and provides you with a $10,000 raise each subsequent day. (For instance, you earn $60,000 on the second day, $70,000 the third day, and so forth.)

Rate Plan C pays 2 cents the first day and doubles every subsequent day. (For instance, you earn 4 cents on the second day, 8 cents on the third day, and so forth)

Payday!

Rate Plan A pays $200,000 a day.

Payday!Rate Plan B pays $50,000 your first day and provides you with a

$10,000 raise each subsequent day. (For instance, you earn $60,000

on the second day, $70,000 the third day, and so forth.)

Payday!Rate Plan C pays 2 cents the first day and doubles every

subsequent day. (For instance, you earn 4 cents on the second day,

8 cents on the third day, and so forth)

Payday!Rate Plan C pays 2 cents the first day and doubles every

subsequent day. (For instance, you earn 4 cents on the second day,

8 cents on the third day, and so forth)

Payday!Rate Plan C pays 2 cents the first day and doubles every

subsequent day. (For instance, you earn 4 cents on the second day,

8 cents on the third day, and so forth)

Exponential Functions

xbxf )(base

Variable is in

exponent

*Just because a function has an exponent, doesn’t mean it is an exponential function

xxxf 43)( 2

123)( xxg

13)( 3 xxh

23)( xth

12

23)( xxf

Basic Graphsxxf 2)(

Basic Graphsx

xf

2

1)(

This is

considered

Exponential Growth

What

common point

do they all

pass through?

This is

considered

Exponential Decay

Exponential Functions with Initial

Values

xbaxf )(

Initial Value,

or initial

population

Rate of

growth or

decay

Some unit of

time (usually)

Exponential Functions with Initial

Values

Initial Value,

or initial

population

Rate of

growth or

decay

Some unit of

time (usually)

trPtP 0)(

…Quick Algebra Check!...

223

3

21 4

A bacteria starts with an initial count of 3000

and doubles every hour.

How many bacteria after 3.5 hours?

When will there be 25,000 bacteria?

A bacteria starts with an initial count of 3000.

An antibiotic is introduced, causing half of the

bacteria to die off each hour.

How many bacteria after 3.5 hours?

When will there be 500 bacteria?

Finding Exponential Functions

Need initial value (0, …), and another

data point (x, y).

Substitute into exponential function:

Solve for the growth/decay rate.

Then rewrite exp. function.

(similar to what we’ve done before)

xbaxf )(

Finding Exponential Functions

Find the exponential function of the

form that passes through the points

(0,100) and (4, 1600)

xbaxf )(

Finding Exponential Functions

A population of bacteria grew from 24

to 615 over the course of 5 hours, find

an exponential function to model this

growth xbaxf )(

Finding Exponential Functions

xbaxf )(

The table shows

consumer credit (billions)

for various years.

Find an exponential

function and estimate

credit for the year 2016

Classwork

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