2Tvwo §7.1 and §7.2

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

Welcome ...

in the first Long distance Lesson!

Thanks to the technical developments you can work on,

for yourself but also a bit together,

right now on this LessonUp.

§7.1 and §7.2 

The following slides are about:

+ from percentage to factor  and

+ exponential growth

In a ratio table it is handy to use the number ....... (fill in).

Answer: the number '1' ! Below you see an example:

Note: '1' is written in the line that contains the other known number: 100.

A factor

1. is a number you add
2. is a building where goods are made by machines and (wo)men
3. is a number you multiply by
4. is a percentage

Factor

Instead of using a ratio table where you go to 1 first, you can use the factor to calculate your answer with one calculation.

Factor

The definition of the factor is the number you multiply an original amount by, to get the new amount:

(original = old)

This rule can also be written like this:

Calculating 40 % of 30 % of 300 litres
means ...

1. taking 70 % of 300 litres
2. 0.4 + 0.3 x 300 litres
3. 0.7 x 300 litres
4. 0.4 x 0.3 x 300 litres

40 % of 30 % of 300 litres
is ....

1. 48 litres
2. 46 litres
3. 36 litres
4. 38 litres

In the next slide first an increase and then a decrease. 

Watch carefully how to tackle this more complicated job!

Percentage of a percentage

Using a factor is useful when an amount changes by a given percentage and is then again changed by a given percentage.

A company increases the price of their 400 euro tv by 12% and then give a discount of 20% on the new price.

Question 1: What is the sale price of the tv?

Question 2: What percentage is the actual discount?

Percentage of a percentage

A company increases the price of their 400 euro tv by 12% and then gives a discount of 20% on the new price.

Question 1: What is the sale price of the tv?        Question 2: What percentage is the actual discount?

 §7.2 Exponential growth (??!)

 Two more slides about §7.2,

with some basic knowledge 

about Exponential growth.

After all, that is what the § is about!

Exponential growth

If you multiply by the same factor everytime for the same increase in units of time, we say there is exponential growth. We even call it this, if the factor you multiply by is between 0 and 1 (so a decrease). If there is exponential growth, we call the factor you multiply by, the growth factor.

Example: The number of bacteria  increase by 50% every day.

Exponential growth

To check if a table or graph corresponds to exponential growth, you have to calculate the growth factor for each pair of consecutive amounts. Because amounts are often rounded off, the growth factor is only approximately the same every time.

Homework time.

If you are stuck and the Solutionsbook is not clear enough for you,  you may mail me. 

As soon as I can I will provide you with some explanation.

                                         [e-mail]

Homework

+  Make and correct §7.2 

+  When you are stuck and the Solutionsbook is not clear enough for you, 

+  you may mail me and I will provide you with an explanation.

                                              [e-mail]