the natural base e is used in banking, algebra homework help

Use the information about banking on

page 556

to explain how the natural base e is used in banking. Include an explanation of how to calculate the value of an account whose interest is compounded continuously, and an explanation of how to use natural logarithms to find the time at which the account will have a specified value in your answer.

9-5
Base e and
Natural Logarithms
Continuously Compounded interest
Main Ideas
• Evaluate expressions
involving the natural
base and natural
logarithms
Solve exponential
equations and
inequalities using
natural logarithms
2
GET READY for the Lesson
Suppose a bank compounds
interest on accounts continuously,
that is, with no waiting time
between interest payments.
To develop an equation to
determine continuously
compounded interest, examine
what happens to the value A of
an account for increasingly larger
numbers of compounding
periods n. Use a principal P of $1,
an interest rate r of 100% or 1,
and time t of 1 year
27145
27181
yeary (3)
Cuarterly (+3
(month)
365
8780
houy (3)
New Vocabulary
natural base,
natural base exponential
function
natural logarithm
natural logarithmic
function
(1)
Base e and Natural Logarithms in the table above, as it increases, the
expression 1(1 + A)”” or (1 + !)” approaches the irrational number
2.71828…. This number is referred to as the natural base, e.
An exponential function with base e is called a
natural base exponential function. The graph of
y = e is shown at the right. Natural base
トーク
exponential functions are used extensively in
science to model quantities that grow and decay
41, el
continuously
Most calculators have an e’ function for
evaluating natural base expressions.
0,1)
o
Study Tip
Simplifying
Expressions
with e
You can simply
expressions involving
e in the same manner
in which you simplify
expressions involving
Examples:
EXAMPLE Evaluate Natural Base Expressions
Use a calculator to evaluate each expression to four decimal places.
a. e2 KEYSTROKES: 2nd (e”] 2 ENTER 7.389056099
027.3891
b. -1.3 KEYSTROKES: 2nd [e”) -13 ENTER 272531793
e-13 0.2725
Check Your Progress
1A.
کع= تم . تج
IB.-22
536 Chantar Enantial and carithmic Relations