CH 4.3 Use Functions Involving e.notebook
CH 4.3 Use Functions Involving e.notebook
Using Functions Involving e
4.3 Use Functions involving e • What is e? • Using e
December 10, 2012
Using Functions Involving e We are going to use a number called e. It is very similar to π. e is named Euler's number or the natural base and is also referred to as a transcendental number.
• Continuously compounded interest.
Dec 91:09 PM
Using Functions Involving e
We can see how e is calculated from the compound interest formula.
Dec 91:09 PM
Using Functions Involving e
Dec 91:09 PM
Dec 91:09 PM
Using Functions Involving e In many ways, we will treat e in the same manner as we deal with a variable such as x.
Dec 91:09 PM
Using Functions Involving e
Dec 91:09 PM
1
CH 4.3 Use Functions Involving e.notebook
December 10, 2012
Using Functions Involving e
Using Functions Involving e
On your calculator, look for the natural log button, which look like this:
The characteristics of the natural base exponential function are the same as the exponential growth and decay, with the following exception.
LN
• The growth rate in a decay equation is written as a negative number.
Hit the 2nd button, and then LN. you should get e^( on your screen. Now type in the exponent and close the parentheses.
Dec 91:09 PM
Using Functions Involving e ØIf is positive then and it is an exponential growth problem.
Decay
Growth
Dec 91:09 PM
Using Functions Involving e The value of an antique car can be modeled with an exponential equation. The car is worth $20,000 today and grows in value at 5.25%. How much is the car worth in 10 years?
ØIf is negative then and it is an exponential decay problem.
Dec 91:09 PM
Using Functions Involving e
Dec 91:09 PM
Using Functions Involving e The value of a boat can be modeled with an exponential equation. The car is worth $7,000 today and depreciates in value at 12.6%. How much is the car worth in 6 years?
Dec 91:09 PM
Dec 91:09 PM
2
CH 4.3 Use Functions Involving e.notebook
Using Functions Involving e
December 10, 2012
Using Functions Involving e When interest in compounded continuously, we use the following equation.
A = final amount P = principal (starting amount) r = interest rate t = time
Dec 91:09 PM
Dec 91:09 PM
Using Functions Involving e
Using Functions Involving e
You deposit $500 into a bank account where the interest of 5.24% is compounded continuously. How much is in you bank account in 3 years if there are no deposits or withdrawls?
Dec 91:09 PM
Dec 91:09 PM
Using Functions Involving e P
Frequency of compounding per year
n
r
t
A
$ 1.00
annual
1
1
1
$ 2.00
$ 1.00
semiannual
2
1
1
$ 2.25
$ 1.00
quarterly
4
1
1
$ 2.44140625
$ 1.00
monthly
12
1
1
$ 2.61303529022468
$ 1.00
weekly
52
1
1
$ 2.69259695443717
$ 1.00
daily
365
1
1
$ 2.71456748202201
$ 1.00
hourly
8760
1
1
$ 2.71812669161742
31536000
1
1
$ 2.71828178130246
1
1
$ 2.71828182845905
$ 1.00 by the second
$ 1.00
continuously continuously
Dec 91:09 PM
Using Functions Involving e 4.3 Use Functions involving e • What is e? • Using e • Continuously compounded interest.
Dec 91:09 PM
3
Attachments
4.3 Continuously Compound Interest.doc
Using Functions Involving e
4.3 Use Functions involving e • What is e? • Using e
December 10, 2012
Using Functions Involving e We are going to use a number called e. It is very similar to π. e is named Euler's number or the natural base and is also referred to as a transcendental number.
• Continuously compounded interest.
Dec 91:09 PM
Using Functions Involving e
We can see how e is calculated from the compound interest formula.
Dec 91:09 PM
Using Functions Involving e
Dec 91:09 PM
Dec 91:09 PM
Using Functions Involving e In many ways, we will treat e in the same manner as we deal with a variable such as x.
Dec 91:09 PM
Using Functions Involving e
Dec 91:09 PM
1
CH 4.3 Use Functions Involving e.notebook
December 10, 2012
Using Functions Involving e
Using Functions Involving e
On your calculator, look for the natural log button, which look like this:
The characteristics of the natural base exponential function are the same as the exponential growth and decay, with the following exception.
LN
• The growth rate in a decay equation is written as a negative number.
Hit the 2nd button, and then LN. you should get e^( on your screen. Now type in the exponent and close the parentheses.
Dec 91:09 PM
Using Functions Involving e ØIf is positive then and it is an exponential growth problem.
Decay
Growth
Dec 91:09 PM
Using Functions Involving e The value of an antique car can be modeled with an exponential equation. The car is worth $20,000 today and grows in value at 5.25%. How much is the car worth in 10 years?
ØIf is negative then and it is an exponential decay problem.
Dec 91:09 PM
Using Functions Involving e
Dec 91:09 PM
Using Functions Involving e The value of a boat can be modeled with an exponential equation. The car is worth $7,000 today and depreciates in value at 12.6%. How much is the car worth in 6 years?
Dec 91:09 PM
Dec 91:09 PM
2
CH 4.3 Use Functions Involving e.notebook
Using Functions Involving e
December 10, 2012
Using Functions Involving e When interest in compounded continuously, we use the following equation.
A = final amount P = principal (starting amount) r = interest rate t = time
Dec 91:09 PM
Dec 91:09 PM
Using Functions Involving e
Using Functions Involving e
You deposit $500 into a bank account where the interest of 5.24% is compounded continuously. How much is in you bank account in 3 years if there are no deposits or withdrawls?
Dec 91:09 PM
Dec 91:09 PM
Using Functions Involving e P
Frequency of compounding per year
n
r
t
A
$ 1.00
annual
1
1
1
$ 2.00
$ 1.00
semiannual
2
1
1
$ 2.25
$ 1.00
quarterly
4
1
1
$ 2.44140625
$ 1.00
monthly
12
1
1
$ 2.61303529022468
$ 1.00
weekly
52
1
1
$ 2.69259695443717
$ 1.00
daily
365
1
1
$ 2.71456748202201
$ 1.00
hourly
8760
1
1
$ 2.71812669161742
31536000
1
1
$ 2.71828178130246
1
1
$ 2.71828182845905
$ 1.00 by the second
$ 1.00
continuously continuously
Dec 91:09 PM
Using Functions Involving e 4.3 Use Functions involving e • What is e? • Using e • Continuously compounded interest.
Dec 91:09 PM
3
Attachments
4.3 Continuously Compound Interest.doc
