1-4 Formulas, exponential growth and percentages (p. 16)

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• Leerjaar 3

1-4 Formulas, exponential growth 

       and percentages (p. 16)

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• Determine the factor when there is exponential growth.
• Determine the formula if you have the table for exponential growth between two variables.

• Use percentages to calculate growth over more than one time interval.
  
• Explain when there is a percentage increase,and when there is a percentage decrease.
  

Percentages

• Exponential growth can be expressed in percentages.
• In this case, the number increases or decreases by the same percentage for each unit of time.
• You multiply by the same 

      factor each time.

26 a to e

26a

1. T=750⋅1,15​t​​
2. T=750⋅0,85​t​​
3. T=1,15⋅750​t​​
4. T=0,85⋅750​t​​

26b

1. F=24000⋅1,45​t​​
2. F=24000⋅5,5​t​​
3. F=24000⋅1,045​t​​
4. F=24000⋅0,945​t​​

26c

1. R=3025⋅0,905​t​​
2. R=3025⋅1,095​t​​
3. R=3025⋅0,5​t​​
4. R=3025⋅0,95​t​​

26d

1. B=1000000⋅0,2​t​​
2. B=1000000⋅2​t​​
3. B=1000000⋅0,02​t​​
4. B=1000000⋅0,98​t​​

26e

1. D=2500⋅1,5​t​​
2. D=2500⋅2,5​t​​
3. D=2500⋅0,5​t​​
4. D=2500⋅1,15​t​​

KBUTXK

Increase or decrease?

• You can use the growth factor to calculate the percentage by which a number increases or decreases per unit of time.
  
• A growth factor g larger than 1 corresponds to a percentage increase. 
  
• A growth factor g between 

       0 and 1 corresponds to a 
      percentage decrease.

29 a to d

29a

1. increase 29%
2. decrease 29%
3. increase 71%
4. decrease 71%

29b

1. increase 20%
2. decrease 20%
3. increase 80%
4. decrease 80%

29c

1. decrease 95%
2. increase 95%
3. decrease 5%
4. increase 5%

29d

1. Increase 9%
2. decrease 9%
3. increase 109%
4. decrease 109%

30 a to c (not mcq)

Conclusion:

• Exponential growth can be expressed in percentages. 

          Increase = (100 + %) / 100

         Decrease = (100 - %) / 100

• Percentage increase - g is larger than 1

       Percentage decrease - g is between 0 and 1

Try on your own

1, 2, 5 and 7

TRY ON YOUR OWN

23, 24, 25, 27, 28 (p. 16)

RULES:

• In your writingbook
• Use: Textbook
• Discussion when you are stuck is allowed

Extra excercise: B7, B8 (p. 27)

Challenge: C4 (p. 30)