A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW:...
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Transcript of A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW:...
![Page 1: A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW: p. 451-454 1-13, 25-55, 65-73 odd.](https://reader030.fdocuments.in/reader030/viewer/2022032802/56649e035503460f94aee5ec/html5/thumbnails/1.jpg)
A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously,
Applications
HW: p. 451-454 1-13, 25-55, 65-73 odd
![Page 2: A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW: p. 451-454 1-13, 25-55, 65-73 odd.](https://reader030.fdocuments.in/reader030/viewer/2022032802/56649e035503460f94aee5ec/html5/thumbnails/2.jpg)
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
![Page 3: A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW: p. 451-454 1-13, 25-55, 65-73 odd.](https://reader030.fdocuments.in/reader030/viewer/2022032802/56649e035503460f94aee5ec/html5/thumbnails/3.jpg)
Is the function exponential?If so, identify the base
3x
2(3)x
1x
42 x
2 x
2x
![Page 4: A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW: p. 451-454 1-13, 25-55, 65-73 odd.](https://reader030.fdocuments.in/reader030/viewer/2022032802/56649e035503460f94aee5ec/html5/thumbnails/4.jpg)
![Page 5: A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW: p. 451-454 1-13, 25-55, 65-73 odd.](https://reader030.fdocuments.in/reader030/viewer/2022032802/56649e035503460f94aee5ec/html5/thumbnails/5.jpg)
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
![Page 6: A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW: p. 451-454 1-13, 25-55, 65-73 odd.](https://reader030.fdocuments.in/reader030/viewer/2022032802/56649e035503460f94aee5ec/html5/thumbnails/6.jpg)
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
![Page 7: A3 4.1 Exponential functions, Compound Interest, Interest Compounded Continuously, Applications HW: p. 451-454 1-13, 25-55, 65-73 odd.](https://reader030.fdocuments.in/reader030/viewer/2022032802/56649e035503460f94aee5ec/html5/thumbnails/7.jpg)
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.