objectives: today we will … 1.write and solve exponential growth functions. 2.graph exponential...

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Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential Growth Functions 8.5

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Page 1: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

Objectives: Today we will …

1.Write and solve exponential growth functions.

2.Graph exponential growth functions.

 

Vocabulary: exponential growth

Exponential Growth Functions8.5

Page 2: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

Would You Rather … ?!?!

• After arguing with your family that you should get a higher allowance your

family offers you two allowance options. Either, they will give you $20 each

week or they will give you one penny on the first day and double your

allowance every day for 31 days. What option would you pick?

Back-up your answer with math!

Page 3: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

The Solution …

1      $.01

2      $.02

3      $.04

4      $.08

5      $.16

6      $.32

7      $.64

8      $1.28

9      $2.56

10      $5.12

11      $10.24

12      $20.48

13      $40.96

14      $81.92

15     $163.84

16     $327.68

17     $655.36

18    $1310.72

19    $2621.44

20    $5242.88

21   $10,485.76

22 $20,971.52

23 $41,943.04

24 $83,886.08

25 $167,772.16

26 $335,544.32

27 $671,088.64

28 $1,342,177.2

8

29 $2,684,354.56

30 $5,368,709.12

31 $10,737,418.24

Page 4: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

Real World Exponential Growth Example

• http://www.mathwarehouse.com/exponential-growth/exponential-models-

in-real-world.php

Page 5: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

Exponential Growth Functions8.5

EXPONENTIAL GROWTH MODEL

A quantity is growing exponentially if it increases by the same percent in each time period.

C is the initial amount. t is the time period.

(1 + r) is the growth factor, r is the growth rate.

Exponential growth always has a growth rate greater than or equal to one. (1 + r) ≥ 1

y = C (1 + r)tSometimes use P instead of C Note: measure of

rate and time MUST be in the same time unit

Page 6: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

Example 1 Compound Interest

You deposit $1500 in an account that pays 2.3% interest compounded yearly,

1)What was the initial principal (C) invested?

2)What is the growth rate (r)? The growth factor?

3)Using the equation y = C(1+r)t, write the equation that models this situation. Then figure out how much money would you have after 2 years if you didn’t deposit any more money?

C or P = $1500

Growth rate (r) is 0.023. The growth factor is 1.023.

y = $1569.79

Page 7: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

Example 2 Compound Interest

A savings certificate of $1000 pay 6.5% annual interest compounded yearly. First, write the

equation that models this situation. Then figure out what is the balance when the certificate

matures after 5 years?

≈ $1370.09

Page 8: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

1.What is the percent increase each year?

2.Write a model for the number of rabbits in any given year.

3.Find the number of rabbits after 5 years.

Example 3 Exponential Growth Model

A population of 20 rabbits is released into a wild-life region. The population triples each year for 5 years.

200%

≈ 4860 rabbits

y =20(1+2.0

0)t

Page 9: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

Exponential Growth Model

Graph the growth of the rabbits.

Make a table of values, plot the points in a coordinate plane, and draw a smooth curve through the points.

t

y 486060 180 540 162020

51 2 3 40

0

1000

2000

3000

4000

5000

6000

1 72 3 4 5 6Time (years)

Po

pu

lati

on

P = 20 ( 3 ) t Here, the large

growth factor of 3 corresponds to a rapid increase

Here, the large growth factor of 3 corresponds to a rapid increase

Example 4

Page 10: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

1.Write a model for the weight during the first 6 week.

2.Find the weight at the end of six weeks.

Example 5 Exponential Growth Model

A newly hatched channel catfish typically weighs about .3 grams. During the first 6 weeks of life, its growth is approximately exponential, increasing by about 10% a day.

y =.3(1+.10)t

≈ 16.4 grams

Page 11: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

Example 6 Exponential Growth Model

Graph

Make a table of values, plot the points in a coordinate plane, and draw a smooth curve through the points.

t

y

0

y =3(1.10)t

Page 12: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

1.Write a model for the number of bacteria at any hour.

2.Find the number of bacteria after 8 hours.

Example 7 Exponential Growth Model

An experiment started with 100 bacteria. They double in number every hour.

y =100(1+1.

00)t≈ 25,600

bacteria

Page 13: Objectives: Today we will … 1.Write and solve exponential growth functions. 2.Graph exponential growth functions. Vocabulary: exponential growth Exponential

• pgs. 480-481 #1, 4, 5, 14, 15, 21, 22, 24

Homework