1. MODELING REAL SITUATIONS USING EXPONENTIAL FUNCTIONS: PART 2 Patterns #5

2. Prerequisites Solve each equation in the list. log 10 = x log 100 = x log 1000 = x log x = 4 log x = 5 How is the change in the logarithm of the number, related to the change in the number itself?

3. Prerequisites-solutions

4. Geography Application A common example of a logarithmic scale is the Richter scale, which is used to measure the intensity of earthquakes. Each increase of 1 unit in magnitude on the Richter scale represents a tenfold increase in the intensity of an earthquake.

5. Example 1 An earthquake occurred on the B.C. Coast in 1700 which measured 9.0 on the Richter scale. In 1989, an earthquake in San Francisco measured 6.9 on the Richter scale. a) How many times as intense as the 1989 San Francisco earthquake was the 1700 B.C. Coast earthquake? b) Calculate the magnitude of an earthquake that is one-quarter as intense as the 1700 B.C. Coast earthquake.

6. Example 1 a) How many times as intense as the 1989 San Francisco earthquake was the 1700 B.C. Coast earthquake?

7. Example 1 b) Calculate the magnitude of an earthquake that is one-quarter as intense as the 1700 B.C. Coast earthquake.

8. Biology Application The last section involved half-life and doubling times. Not all situations are multiples of 2: In favourable breeding conditions, the population of a swarm of desert locusts can multiply tenfold every 20 days

9. Biology Application We can modify the equation for half –life to become:

10. Example 1 A swarm of desert locusts can multiply tenfold every 20 days. a) How many times as great is the swarm after 12 days than after 3 days? b) Calculate how long it takes for the population of the swarm to double.

11. Example 2 a) How many times as great is the swarm after 12 days than after 3 days?

12. Example 2 b) Calculate how long it takes for the population of the swarm to double.

13. Example 3 A population of insects can multiply tenfold in 30 days. a) How many times as great is the population after 20 days than after 8 days? b) Calculate how long it takes for this population to double.

14. Example 3 a) How many times as great is the population after 20 days than after 8 days?

15. Example 3 b) Calculate how long it takes for this population to double.

16. Textwork p.98/1-21