1. Produced by MEI on behalf of OCR © OCR 2013 Introduction to Quantitative Methods Exponential Growth and Decay

2. Produced by MEI on behalf of OCR © OCR 2013 Interest on savings £20 000 is put into savings which pay 3% interest every year. What is the multiplier? How much will there be in the savings account after 5 years?

3. Produced by MEI on behalf of OCR © OCR 2013 Interest on savings £20 000 is put into savings which pay 3% interest every year. How much will there be in the savings account after 5 years? The multiplier for an increase of 3% is 1.03 The amount after 5 years is 20 000 x 1.03 5 To the nearest penny, this is £23185.48

4. Produced by MEI on behalf of OCR © OCR 2013 Question £15 000 is put into savings which pay 5% interest every year. How much will there be in the savings account after 3 years? Answer 15 000 x (1.05) 3 = £17364.38

5. Produced by MEI on behalf of OCR © OCR 2013 Growth This means the amount of money is growing every year by a factor of 1.05 15 000 x (1.05) 4 = 15 000 x 1.05 x 1.05 x 10.5 Every year the money is being multiplied by the same amount. 1 year2 years3 years

6. Produced by MEI on behalf of OCR © OCR 2013 Growth When there is a multiplier and every year (month, week….) the amount is increasing by the same multiple this is called Exponential Growth

7. Produced by MEI on behalf of OCR © OCR 2013 General Expression The start amount is £15 000 How would you find the amount of money after 5 years? 6 years? 10 years? n years

8. Produced by MEI on behalf of OCR © OCR 2013 Exponential Growth How many great, great, great grandparents do you have? ParentsGrand parents Great grand Parents Great, Great Grandparents Great, Great Great Grand Parents 2481632 x 2

9. Produced by MEI on behalf of OCR © OCR 2013 Exponential Growth So you have 2 x 2 x 2 x 2 x 2 = 2 5 great, great, great grandparents What is the multiplier in this case? 2 If g is the number of generations back from yourself what is the formula? 2g2g

10. Produced by MEI on behalf of OCR © OCR 2013 Depreciation Sometimes the amount gets smaller every year…

11. Produced by MEI on behalf of OCR © OCR 2013 Depreciation A new car costs £16 000. It depreciates by 15% a year How much is it worth in 4 years? The multiplier for a decrease of 15% is 0.85 The amount after 4 years is 16 000 x 0.85 4 This is £8353.10

12. Produced by MEI on behalf of OCR © OCR 2013 Getting Less The money is getting less each year by a factor of 0.85 16 000 x 0.85 4 = 16 000 x 0.85 x0.85 x 0.85 x 0.85 Every year the money is being multiplied by the same amount. I year2 years 3 years4 years

13. Produced by MEI on behalf of OCR © OCR 2013 General Expression How would you find the amount of money after 5years? 6 years? 10 years? n years? Answer 16 000 x (0.85) 5 16 000 x (0.85) 6 16 000 x (0.85) 10 16 000 x (0.85) n

14. Produced by MEI on behalf of OCR © OCR 2013 Getting Less When there is a multiplier and every year (month, week….) the amount is decreasing by the same multiple this is called Exponential Decay

15. Produced by MEI on behalf of OCR © OCR 2013 Exponential Decay There are 64 players in a tennis tournament. When a player loses he is out of the tournament. How many rounds until the final? RoundPlayers 164 232 316 48 54 62

16. Produced by MEI on behalf of OCR © OCR 2013 Exponential Decay So the number of players goes down every round 64 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 64 x 0.5 5 = 2 There are 5 rounds till the final when there will be 2 players left. What is the multiplier in this case? Answer 0.5

17. Produced by MEI on behalf of OCR © OCR 2013 Exponential Growth and Decay What do you notice about the multipliers for Exponential growth? Exponential Decay? The multiplier is greater than 1 for growth and less than 1 for decay.

18. Produced by MEI on behalf of OCR © OCR 2013 Examples Do these represent exponential growth or decay 1.100 x (2) x 2. 50 x (0.9) n 3. 25 x (1.01) t growth decay growth

19. Produced by MEI on behalf of OCR © OCR 2013 Examples Write down 3 more statements for growth and 3 more statements for decay