Docstoc

02.06.12_02.07.12 Exponential Growth and Decay

Document Sample
02.06.12_02.07.12 Exponential Growth and Decay Powered By Docstoc
					                                       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   About 12 years
                    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

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:12
posted:4/9/2012
language:
pages:1