a3 4.1 exponential functions, compound interest, interest compounded continuously, applications hw:...
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A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously,
Applications
HW: p. 451-454 1-13, 25-55, 65-73 odd
Exponential Function – a little more info…
initial amount ( 0)
base (growth or decay factor) ( 0 and 1)
xy ab
a a
b b b
1Natural Base (1 )ne
n
Is the function exponential?If so, identify the base
3x
2(3)x
1x
42 x
2 x
2x
TransformationsTransformation Equation Description
Vertical Translation Down c
Up cHorizontal Translation Left c
Right cReflection Over y axis
Over x axisVertical Stretch/Shrink Stretch by c |c|>1
Shrink by c |c|<1Horizontal Stretch/Shrink Stretch by 1/c |c|<1
Shrink by 1/c |c|>1
( ) xg x b c ( ) xg x b c
( ) x cg x b
( ) x cg x b
( ) xg x b
( ) xg x b
( ) xg x cb
( ) cxg x b
Interest Formulas
Simple Interest: big ticket items – cars, boats, houses
Compound Interest: investments, credit cards, legal extortion…
Interest Compounded Continuously
PrI t
(1 )tA P r (1 )ntr
A Pn
rtA Pe
Examples1. You decide to invest $8000 for 6 years and you have a choice
between 2 accounts. The first pays 7% per year compounded monthly. The second pays 6.85% per year, compounded continuously. Which is the better investment?
2. A sum of $10,000 is invested at an annual percentage rate of 8%. Find the balance in the account after 5 years, subject to quarterly compounding and continuous compounding.