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Math114
Chapter5sec5
ExponentialGrowthandDecayRatesandCompoundinterest
Clark
Exponentialgrowthanddecayareoftenmeasuredasapercentagechangeperyearorothertime
period.
Definition:Growthordecayrate:Thepercentagechangeinaquantityper1unitoftimeiscalled
thegrowthordecayrate’r’.
b=1+r
r=b–1
where‘r’isapercentagewrittenasadecimaland‘b’isthebaseofanexponentialfunctionofthe
form,f(x)=a•b x Page464
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Math114
Page 2 of 2
Clark
SimpleandCompoundInterest
SimpleInterestformula:A=P+Prt
Calculatetheaccountbalance‘A’after‘P’dollarshavebeeninvestedfor‘t’years.
⎛
r⎞
nt
CompoundInterestFormula: A = P ⎜ 1+ ⎟ ⎝ n⎠
n=1,sincetheinterestwillbecompoundonlyonceayear.
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CompoundContinuouslyformula:A = Pert A–accountbalanceaftertheprincipal‘P’hasbeeninvestedatanannualrate‘r’
compoundedcontinuouslyfor‘t’years.
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