Section 5-1. Today, we will apply exponential functions to solve problems. Do you remember recursive formulas? Because you will need to use them!

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Presentation transcript:

Section 5-1

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

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

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

Find the first three terms of the recursive formula

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

p240 #2b, #3a

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

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

p240 #4 all – just find percent change

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

In 1991, the population of the People’s Republic of China was 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 Year Pop

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 = 1.151(1.015) 1 (1992, 1.168) (2000, 1.316) = 1.151(1.015) 9  

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.