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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. u0 16 y-intercept un (1 .25)un 1 Growth rate Percent change Write an equation for the recursive formula. u0 16 Remember from yesterday: un (1 .25)un 1 f(x) = abx f ( x) 16(.75) x Find the first three terms of the recursive formula u0 16 un (1 .25)un 1 0 16 1 2 3 Evaluate the following equation at x = 0, x = 1, x = 2, and x = 3. f ( x) 16(.75) x f(x) 0 1 2 x 3 p240 #2b, #3a 2b. 24, 36, 54 f ( x) 24(1.5) x 3a. f(0) = 125, f(1) = 75, f(2) = 45 u0 125 u1 (.6)un 1 How do you determine percent increase or decrease? 2nd # - 1st # 1st # 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 1.151 billion, with a growth rate of 1.5% annually. Write a recursive formula to model this growth. u0 1.151 un (1 .015)un 1 Complete a table recording the populations for the years 1991-2000. Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Pop. 1.151 1.168 1.186 1.204 1.222 1.240 1.259 1.277 1.297 1.316 Define the variables and write an exponential equation that models this growth. Choose two table points and see if it works. Define variables Check (1992, 1.168) Independent (x) = Dependent (y) = YEAR POPULATION Write an equation 1.168 = 1.151(1.015)1 (2000, 1.316) 1.316 = 1.151(1.015)9 f(x) = 1.151(1.015)x 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.