Exponential functions (t3g)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Exponential functions

March 24th

t3g

11:00

Camera ON

Schedule

• Announcements                                             5 min
• Review: trigonometry                                 10 min
• Exponential functions                                15 min
    Quiz questions
• Practice                                                             20 min
    Break-out rooms
• Discuss exercise                                            10 min

Programme

Ch.8.1/8.2 today

Review Monday

Test ch.3

Redo (max grade 5.5):

    Thursday, April 13th, 5th period

Are you in steunuur? Mandatory anyway

Test answers ch.4-6-7.1

Video in Teams!

Files - Lesmateriaal - Answers test ch.4-6-7

Last lesson's

Intended Learning Outcomes

At the end of the lesson you could...

1. Apply trigonometric calculations in contexts and situations

You want to know
the length of LM.
What do you use?

1. Tangent
2. Sine
3. Inverse sine
4. Inverse cosine

You want to know
the size of
What do you use?

∠A.

1. Tangent
2. Sine
3. Inverse sine
4. Inverse cosine

You want to know
the length of KM.
What do you use?

1. Inverse sine
2. Sine
3. Inverse tangent
4. Cosine

Today's

Intended Learning Outcomes

At the end of the lesson you can...

1. Set up your own exponential formula
2. Recognize and apply exponential growth vs. decay
3. Combine percentages with exponential formulas

Formulas:

linear vs. exponential

Formulas:

linear vs. exponential

a = gradient                                                    g = growth factor

b = y-intercept                                              b = initial value

y=ax+b

N=b⋅g​t​​

Example

linear vs. exponential

__________________________________________________________________

2 = gradient                                                                         2 = growth factor

5 = y-intercept                                                                   5 = initial value

y=2x+5

N=5⋅2​t​​

Example

linear vs. exponential

__________________________________________________________________

2 = gradient                                                                         2 = growth factor

5 = y-intercept                                                                   5 = initial value

y=2x+5

N=5⋅2​t​​

Exponential formulas

Describe (in general terms) what you think happens to the graph when:

a. g > 1

b. 0 < g < 1

b. g < 0

N=b⋅g​t​​

Describe what you think happens to the graph when:
a. g > 1
b. 0 < g < 1
b. g < 0

N=b⋅g​t​​

www.geogebra.org/graphing

Growth factor

g > 1: only increasing

0 < g < 1: only decreasing

g < 0: impossible

N=b⋅g​t​​

Link with percentages

Percentages can also be written as a growth factor!

Example:

When you keep increasing a price by 25%, 

you're doing                   each time

⋅1.25

Link with percentages

Percentages can also be written as a growth factor!

Example:

When you keep decreasing a price by 14%, 

you're doing                   each time

⋅0.86

Anouk starts with 500 euros in the bank. She receives a positive 2% interest rate per year.
N is amount of money, t is time in years.
What is the formula for this situation?

1. N=2⋅500​t​​
2. N=500⋅2​t​​
3. N=1.02⋅500​t​​
4. N=500⋅1.02​t​​

Thirza starts with 200 euros in the bank. She loses 13% each month due to a gambling addiction. :(
What is the corresponding formula?
Again: N is amount of money, t is time in months.

1. N=200⋅0.13​t​​
2. N=200⋅13​t​​
3. N=200⋅0.87​t​​
4. N=200⋅87​t​​

Practice

                                   Chapter 8

                                  Everyone:

                                Do 2, 5 and 8

                                 Afterwards:

Math A/C

Do 9, 10, 13, 14,
      15, 16 and 18

Math B/D

Do 9, 10, 13, 16 and 18