# 02.06.12_02.07.12 Exponential Growth and Decay by lanyuehua

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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.
Amount of
Years                                                                                                              Interest
Account Balance (Y)
(X)                                                                                                             Earned that
Year
0           \$1,000                                                                                               \$0
1           1(\$1000) + (0.08)(\$1,000) = 1.08 (\$1,000)                                                            \$80
2           1 (1.08)(\$1,000) + (0.08) [(1.08)(\$1,000)] = 1.08 [1.08 (\$1,000)] = (1.08)2(\$1,000)                  \$86.40
3           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)               \$93.31

x        (1.08)x(\$1,000)
 Equation:
 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)                                             o   200 = 100 (1.06)t
t                                                                          o   200/100 = (1.06)t
o Let a = initial amount / principal
o Let t = time                                             EXPONENTIAL DECAY: y = a (1 + r) t
o Let r = growth rate                                              o Same formula, but the rate is negative
    After 20 years, how much money would I have                     I bought a computer for \$2,000, but it loses
accrued in the bank?                                               value at a rate of 56% annually. How much is it
20
o y = (1000)(1+0.08) = \$4,660.96                              worth after 1 year, 2 years, 3 years, and 4 years?
 I earned \$3660.09 just by                             Years                   Worth (y)
letting money sit in the bank!                       (x)
    If you deposited \$100 worth of birthday money                      0          2000 (1-0.56)0 = 2000 (0.44) 0= 2000
in your savings account and earned 6% interest                                (1) = 2000
compounded annually, how much would you                            1          2000 (0.44) 1= \$880
have in the bank after 1 year, 2 years, 5 years,                   2          2000 (0.44) 2= \$387.20
and 10 years?                                                      3          2000 (0.44) 3= \$170.37
o y = 100 (1 + 0.06)x = 100 (1.06)x                           4          2000 (0.44) 4 = \$74.96
Year (x)     Balance (y)                                                o Show what the graph would look like.
1                       1
100(1.06) = \$106                                   I bought a car that costs \$26,000. It loses value
2            100(1.06)2 = \$112.36                                  at a rate of 20% annually. How much will it be
5                       5
100(1.06) = \$133.82                                   worth after 5 years?
10                      10
100(1.06) = \$179.08                                        o y = 26,000 (1 + -0.2) 5
    How long would it take for your money to                                o     = 26,000 (0.8) 5
double?                                                                 o     = 8,519.68
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

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