1. Section 5-1

2. Today, we will apply exponential functions to solve problems. Do you remember recursive formulas? Because you will need to use them!

3. Let’s review recursive formulas. y-intercept Growth rate Percent change

4. Write an equation for the recursive formula. Remember from yesterday: f(x) = ab x

5. Find the first three terms of the recursive formula 0123 16

6. Evaluate the following equation at x = 0, x = 1, x = 2, and x = 3. x0123 f(x)

7. p240 #2b, #3a

8. 2b. 24, 36, 54 3a. f(0) = 125, f(1) = 75, f(2) = 45

9. How do you determine percent increase or decrease? 2 nd # - 1 st # 1 st #

10. p240 #4 all – just find percent change

11. 4a. 25% decrease 4b. 33 1/3 % increase 4c. 6% decrease 4d. 6.38% increase

12. In 1991, the population of the People’s Republic of China was 1.151 billion, with a growth rate of 1.5% annually. Write a recursive formula to model this growth. Complete a table recording the populations for the years 1991-2000. Year1991199219931994199519961997199819992000 Pop.1.1511.1681.1861.2041.2221.2401.2591.2771.2971.316

13. Define the variables and write an exponential equation that models this growth. Choose two table points and see if it works. Define variables Independent (x) = Dependent (y) = Write an equation YEAR POPULATION f(x) = 1.151(1.015) x Check 1.168 = 1.151(1.015) 1 (1992, 1.168) (2000, 1.316) 1.316 = 1.151(1.015) 9  

14. Work with your partner to complete #6 on p241 skip e. Here are some hints to help you out: a.You need to find the percent change. b.What should your exponent be if a whole day starts at 8:00 am and he is measuring at 8:00 pm? c.What should your exponent be if you are measuring at 12:00 noon? d.If the plant starts at 2.56 cm tall, how tall will it be when it doubles? Guess and check to find the exponent that gives you this height.