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.