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Section 1.5 Exponential Functions Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Investment Choices • You have $1000 to invest. Broker A offers a $100 annual return. Broker B offers an 8% annual compounded return. Which broker do you prefer? • How would your answer change if the returns were different? • How would your answer change if the compounding period changed? Applied Calculus ,4/E, Deborah HughesHallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Population Growth The population of Nevada from 2000 to 2006 is given in Table 1.30. To see how the population is growing, we look at the absolute increases in population in the third column and relative increases in the fourth column. Is the growth linear or exponential? Why? Write a formula that captures the trend of the data. Table 1.30 Population of Nevada (estimated) 2000 – 2006 Year Population (thousands) Change in population (thousands) Relative change in population 2000 2,020 73 3.6% 2001 2,093 75 3.6% 2002 2,168 78 3.6% 2003 2,216 81 3.7% 2004 2,327 84 3.6% 2005 2,411 87 3.6% 2006 2,498 Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved where is the population of Nevada years after 2000. Applied Calculus ,4/E, Deborah HughesHallett Copyright 2010 by John Wiley and Sons, All Rights Reserved …And, a has to be positive. Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Figure 1.61: Exponential growth: P = at , for a > 1 Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Figure 1.62: Exponential decay: P = at , for 0 < a < 1 Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Problem 6 A product costs $80 today. How much will the product cost in t days if the price is reduced by (a) $4 a day = 80 − 4 (b) 5% a day = 80 × 0.95 Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Sales at a company are changing according to the formula S = 1000(0.82)t , where S is sales in thousands of dollars and t is measured in years. Sales at this company are: (a) Increasing by 82% per year (b) Increasing by 82 thousand dollars per year (c) Decreasing by 82% per year (d) Decreasing by 82 thousand dollars per year (e) Increasing by 18% per year (f) Increasing by 18 thousand dollars per year (g) Decreasing by 18% per year (h) Decreasing by 18 thousand dollars per year ConcepTest • Section 1.5 • Question 4 Let f(x) = abx, b > 0. Then (a) bh (b) h (c) bx+h − bx (d) a ConcepTest • Section 1.5 • Question 10 f (x h) f (x)