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Exponential Growth and Decay Formula: Initial Starting Value # of times it grows or decays y ab x Growth/Decay Rate Exponential Growth y ab x b 1 growth rate 1 rate as a decimal $10 is invested in a savings account where is grows 5% per year. y (10)(1 0.05) x 100 90 80 y 10(1.05) x 70 60 50 What is the y –intercept? Would y = 10(1.5)x be above or below this graph? 40 30 20 10 10 20 30 40 50 Exponential Decay y ab x 1 rate as a decimal 0decay brate 1 10 grams of a particular liquid decays at a rate of 75% per day. 11 y (10)(1 0.75) y 10(0.25) x 10 9 8 x 7 6 5 4 3 2 1 1 2 3 4 5 Practice: Monthly benefits for Social Security in May 1992 were $23,307 million. Since then, benefits have increased about 5.4% per year. a) Write an exponential function to model the growth of monthly Social Security benefits paid each year. (use millions in your answer!) y = 23,307(1+0.054)x y = 23,307(1.054)x b) If benefits continue to grow at this rate, when will the monthly Social Security benefits reach $50,000 million? 50,000 = 23,307(1.054)x 1)Graph y = 23,307(1.054)x and y = 50,000 2) Solve 2.14527 = 1.054x through guess and check In 1984, funds for the Emergency Food Assistance program were about $1,075 million. Since 1984, this fund has decreased about 19% per year. a) Write an exponential function to model this situation. Y= 1,075(1 - 0.19)x y = 1,075(0.81)x There is 81% of the fund LEFT each year b) Estimate the funds available for the Emergency Food Assistance program this year. Y = 1075(0.81)24 6.839 million Or graph the equation and TRACE with x = 24