1. Produced by MEI on behalf of OCR © OCR 2013 Introduction to Quantitative methods Using logarithmic scales © OCR 2014

2. Produced by MEI on behalf of OCR © OCR 2013 Example from exponentials This example was taken from the working with exponentials section. The graph shows a model for the number of mobile phone users in an area from 1990 to 2000. © OCR 2014

3. Produced by MEI on behalf of OCR © OCR 2013 Graph © OCR 2014

4. Produced by MEI on behalf of OCR © OCR 2013 It is difficult to see the values in the first few years because they are very small. Since the numbers are getting very big on the y – axis, look at the graph with a logarithmic scale on that axis. © OCR 2014

5. Produced by MEI on behalf of OCR © OCR 2013 Logarithmic graph Year Number of mobile phone users © OCR 2014

6. Produced by MEI on behalf of OCR © OCR 2013 Using the graph Using the graph can you work out what the number of mobile phone users was in 1990? Reading from the graph in 1990 the number of mobile phone users is approximately half way between 100 and 1000 That is half way between 10 2 and 10 3 © OCR 2014

7. Produced by MEI on behalf of OCR © OCR 2013 1000 10 3 100 10 2 Half way between 10 2 and 10 3 is 10 2.5 10 2.5 = 316 © OCR 2014

8. Produced by MEI on behalf of OCR © OCR 2013 The actual value for the number of phone users in 1990 was 285. Do you think using the logarithmic scale gives you a good estimate? Where on the scale would 285 be? 10 2.455 = 285 © OCR 2014

9. Produced by MEI on behalf of OCR © OCR 2013 Example 2 The spreadsheet chart on the next slide shows the population of African black rhinos from 1970 to 1995. What is the approximate population of African black rhinos in 1990? © OCR 2014

10. Produced by MEI on behalf of OCR © OCR 2013 1970 19801990 Year © OCR 2014

11. Produced by MEI on behalf of OCR © OCR 2013 What is the approximate population in 1990? In 1990 the population is approximately 0.6 of the way between 1000 and 10000 That is 0.6 of the way between 10 3 and 10 4 This is 10 3.6 = 3891 © OCR 2014