Wednesday, September 29, 2010

Lesson 15- Eponential Growth and Decay

In this lesson there are two different formulas:

The most common formula to use is:
F= IR^ t/p                    F: final amount       I: initial amount     R: rate of growth ( 5% = 0.05 +1 R>1)   growth decay ( 5%  R= 0.95 - goes down 5)     t: time       p: time for R to occur ( days, weeks, months,etc)  
* note: t and p must be in same units

The second formula is only used for continuous interest rates:
 P= Po e^ Kt          P: final amount       Po: initial amount      e: calculator function   K: growth/decay (no 1)  
t: time 


Example 1:

What will $3500 grow to, if invested at 6% interest for 10 years, compounded monthly?
F= IR ^ t/p               F=?     I= 3500   R= 1.005  t= 10    p=1/12   
(*note: if p is a fraction take the reciprocal and multiply it to the top number) 
F= 3500(1.005)^10/(1/12)
F= 3500(1.005)^120
F= $6367.88

Example 2:

What amount of money would grow to $ 4000 if invested at 91/4%, compounded annually for 4 years?
F= IR ^ t/p              F= 4000   I= ?   R= 1.0925   t= 4     p=1
4000   =     I  (1.0925) ^ 4/ 1
(1.0925)^4     (1.0925)^4
I= $2807.85

Example 3:
P= 100(0.87)^n represents the percent of caffeine in your body n hours after consumption. Write this equation as an exponential function with 1/2 as the base instead of 0.87
R= 0.87  (down) 13% per hr
0.5 = 0.87^ t                   
log0.5   =   t log0.87         1) log both sides
log0.87      log0.87
5  = t






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