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02.06.12_02.07.12: Exponential Growth and Decay *students will model real world situations to develop the exponential growth (and decay) function. 1. Students will work on the “try it out” scientific notation problem and 5 exponent practice problems. Demonstrate on the calculator 2. Grade “Practice with Scientific Notation”. 3. Exponential Growth and Decay If I deposited $1,000 in my savings account at the bank and I earned 8% interest, compounded yearly, how much would my savings increase over time? o Terms: annual interest, compound interest (interest calculated on both the principal (initial amount) and the accrued interest. Make a table. Years (X) Account Balance (Y) 0 1 2 3 x Amount of Interest Earned that Year $1,000 1($1000) + (0.08)($1,000) = 1.08 ($1,000) 1 (1.08)($1,000) + (0.08) [(1.08)($1,000)] = 1.08 [1.08 ($1,000)] = (1.08)2($1,000) 1[(1.08)2($1,000)] + 0.08 [(1.08)2($1,000)] = 1.08 [(1.08)2($1,000)] = (1.08)3($1,000) $0 $80 $86.40 $93.31 (1.08)x($1,000) Equation: 𝑦 = (1,000)(1.08)𝑥 Account balance = (principal/initial amount) [1 + rate (as a decimal)]time Show what the graph looks like on the calculator. EXPONENTIAL GROWTH: y = a (1 + r) t o o o 200 = 100 (1.06)t 200/100 = (1.06)t About 12 years o Let a = initial amount / principal EXPONENTIAL DECAY: y = a (1 + r) t o Let t = time o Same formula, but the rate is negative o Let r = growth rate I bought a computer for $2,000, but it loses After 20 years, how much money would I have value at a rate of 56% annually. How much is it accrued in the bank? worth after 1 year, 2 years, 3 years, and 4 years? o y = (1000)(1+0.08)20 = $4,660.96 Years Worth (y) I earned $3660.09 just by (x) letting money sit in the bank! 0 2000 (1-0.56)0 = 2000 (0.44) 0= 2000 If you deposited $100 worth of birthday money (1) = 2000 in your savings account and earned 6% interest 1 2000 (0.44) 1= $880 compounded annually, how much would you 2 2000 (0.44) 2= $387.20 have in the bank after 1 year, 2 years, 5 years, 3 2000 (0.44) 3= $170.37 and 10 years? 4 2000 (0.44) 4 = $74.96 o y = 100 (1 + 0.06)x = 100 (1.06)x o Show what the graph would look like. Year (x) Balance (y) 1 I bought a car that costs $26,000. It loses value 1 100(1.06) = $106 2 at a rate of 20% annually. How much will it be 2 100(1.06) = $112.36 5 worth after 5 years? 5 100(1.06) = $133.82 10 o y = 26,000 (1 + -0.2) 5 10 100(1.06) = $179.08 o = 26,000 (0.8) 5 How long would it take for your money to o = 8,519.68 double? t o y = 100 (1.06) Other examples: cost of health care, growth of a colony of bacteria, population increase, increase in college tuition, etc. HW 3.12: Exponential Growth and Decay On Thursday students will take a practice EOC in study labs. 3.2 Quiz on Friday, 2/10, and Mon, 2/13