ALGEBRA, Special Functions, Systems of Equations, and Solving systems of equations, algebra homework help

Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it.Page 556 attached.

9-5Base e and
Natural Logarithms
Main Ideas
Continuously Compounded Interest
А
• Evaluate expressions
involving the natural
base and natural
logarithms.
• Solve exponential
equations and
inequalities using
natural logarithms.
2
A=P(1+4)”
n
2.4414…
-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.
2.6130…
1201)
2.7145…
(yearly) 1(1+””
(quarterly) 1(1+2) “”
(monthly) 1(1+)
305)
2.7181…
New Vocabulary
875001)
365
(daily)
8760
(hourly 1(1+0)
natural base, e
natural base exponential
function
natural logarithm
natural logarithmic
function
Base e and Natural Logarithms In the table above, as n increases, the
expression 1(1 + 2)””
) or (1 + )” approaches the irrational number
2.71828…. This number is referred to as the natural base, e.
+
y
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
exponential functions are used extensively in
science to model quantities that grow and decay
continuously.
ve
e’ = e
(1. e)
e = 1
0.1)
o
x
Most calculators have an er function for
evaluating natural base expressions.
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