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Unformatted text preview: 1.5 Exponential Functions and Compounding I What is the yintercept‘? What happens as x —) oo , x —> —oo? t r An exponential function has a constant ratio, while linear functions has a constant difference.
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3/ 2 6 18 54 162 486 [3“] " 1“ t ‘1 An exponential function has an equation:
)2 = Paa‘ . What is an equation for the exponential function listed above? Exponential models are very useful for many models, including how money grows.
Let’s take $1000 and let it grow by 6% per year under different forms of compounding
for 40 years. Simple Interest: no compounding /
A =(Pr)t+P=mt+b \ Annual Compounding
You get interest once per year and calculate the interest off the balance from the prior period. g! / [ lvaM{ﬁ 94 WW taleii) ,_.. O. 0;.) ) Monthly Compounding
You get interest once per month (but only 1i’12th of it) and calculate the interest off the balance from the prior period. {7:09
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A=P[1+E] {1:20 1.6 The Natural Log Ex. 10" 210.00. This can be solved with any base of logarithm, each of which makes the
am; or look different, but are mathematically equivalent. " Mm x:lasﬂDDli)
y 3 luaHJOOTB / '3 gives us now all 4 log rules:
1) logurB) = Iog(A) + log(B)
2) log(A/B) = log (A) — log (B) k 3) log(Aa) = Blog(A) 4) loga(3)=ﬂ=1°33 =1°gx 1 1a Ioga 103x“
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 Fall '11
 Intro

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