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Warm-up (Hint: not all answer will be used) 1.Which equations below model exponential growth? 2.Which equations model exponential decay? A. y = 4 x B. y = 3(0.6) x C. y = -5 x D. y = 3x E. y = ½ (8 x ) F. y=10 x G. y = 1 x H. y = 2.5(0.2) x I. y = 3x 2 A. B. E.F. H.

Homework Answers

Lesson 10-6A Objective: Solve problems involving exponential growth

General Growth Formula y = b = initial amount, starting amount a = growth factor x = time b a x

Example #1 The population of a certain strain of bacteria grows according to the formula y = b(2) x, where x is the time in hours. If there are now 50 bacteria, how many will there be in 2 days (48 hours)? y = b a x y = y = 1.41 x ≈ 14,100,000,000,000,000

Example #2 If the number of rabbits in a cage quadruples (x4) every year, how many will be in the cage after 6 years if you start out with 2? y = b a x y =24 6 y = 8,192

Percentage Growth Formula y = b = initial amount r = % growth (as a decimal) x = time b (1 + ) x r

Example #3 In 2004, the number of weekly passes sold by Tri-Cities Transit was 98,481 and was growing at a rate of 3.8% per year. At this rate, estimate the number of passes sold in y = b(1 + r) x y =98481(1 + ) y = 98481(1.038) 3 y = 110,139

Example #4 In 2001, the population of Lagos, Nigeria was about 7,998,000. Use the population growth of 4.06% per year to estimate the population in 2009? y = b(1 + r) x y = (1 + ) y = (1.0406) 8 y = 10,996,436

Compound Interest Formula A = P = Principal (what you invest) r = interest rate (as a decimal) n = number of times interest is compounded per year t = years P (1 + ) n r n t

Quarterly: n= 4 Semi-annually: n=2 Monthly: n=12

Example #5 If you invest $500 compounded monthly for 10 years at an interest rate of 6%, what will your total investment be worth? P(1 + ) n r n t A = 500 (1 + ) (10) A = A = 500(1.005) 120 A = $909.70

Example #6 Determine the amount of an investment if $1000 is invested at an interest rate of 4% compounded semi-annually for 5 years. P(1 + ) n r n t A = 1000 (1 + ) (5) A = A = 1000(1.02) 10 A = $

Assignment: 10-6 A p. 563 #9-13, 14, 15, 18, 21 Quiz (10-5 and 10-6) on Friday!