Exponential Functions Section 5.1. Evaluate the exponential functions Find F(-1) Find H(-2) Find...
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Transcript of Exponential Functions Section 5.1. Evaluate the exponential functions Find F(-1) Find H(-2) Find...
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
Page 435 50, 54, 58 - 64