Exponential Functions

Section 5.1

Evaluate the exponential functions

x-13 H(x) 8

1 G(x) 5)(

xxxF

Find F(-1)5

15)1( 1 F

Find H(-2) 273)2( 3 H

Find )3

2(G

3

2

8

1)

3

2(

G

3

2

1

8)

3

2(

G 42)

3

2( 2 G

Find F(0) – H(1) 01135)1()0( 110 HF

Natural Base = e

e is an irrational numbere is the base used in continuous

compounded interest problemsExponential FunctionFind f(3)

...71828.2e

xexf )(

09.20)3( 3 ef

Steps to Graph Exponential Function

1. Find y intercept f(0)

2. Find 2 additional points above and 2 below intercept

3. Horizontal asymptote (x axis unless shifted)

4. As x increases1. If b>1 then f(x) increases

2. If 0 < b < 1 then f(x) decreases

xbxf )(

Graph xxf 2)(

Graph xxf 2)(

x

xf

2

1)(

Graph 12)( xxf

Graph 12)( xxf

Graph xexf )(

Graph xexf )(

Graph 5)( 1 xexf

Graph 52)( 3 xexf

52)( )3(1 xexf

Homework

Day 2 Section 5.1

Doubling Time Growth Model

d

t

PP 20

0P = Population at initial time (time = 0)

P= Population at time t

d = doubling time

t = time

Doubling time example

The current population of the island of Doon is 500,000 and it is expected to double in 15 years. Estimate the population in 5 years.

d

t

PP 20

15

5

2000,500 P

0P = 500,000 d = 15, t = 5

26.1000,500 P

000,630P

Half- life

Half-life Model

h

t

AA

2

10

0A = initial amount (time = 0)

A= Amount at time t

h = half-life in years

t = time

Half- life example

A radioactive isotope has a half-life of 119.77 days. If 200 milligrams are given to a patient, how many milligrams are left after 30 days?

h

t

AA

2

10

Compound Interest

P= Principal

r= rate

n= number of times it is compounded in a year

t= number of yers

A= amount after t years

nt

n

rPA

1

Example of compound interest

If $10,000 is deposited in an account paying 4.5% compounding weekly, how much will you have in the account in 3.5 years?

Continuous Compound Interest

P= principalr= ratet= number of yearsA= amount after t years

rtPeA

Example Compounded Continuously

If 10,000 is deposited in an account paying 4.5% compounded continuously, how much will you have in the account in 3.5 years?

Homework

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