Please complete the following questions. It is important that youshow all work you did to solve the problems when you submit your work.This includes any calculations, diagrams, or graphs that helped yousolve it.
OPEN ENDED Give an example of a quantity that growsor decays at a fixed rate. Write a real-world problem involving therate and solve by using logarithms.Writing in Math Use the information aboutbanking on page 556 to explain how the natural base e is used inbanking. Include an explanation of how to calculate the value of anaccount whose interest is compounded continuously, and an explanation ofhow to use natural logarithms to find the time at which the accountwill have a specified value in your answer. Page 556 is in the attachments. Continuously Compounded Interest
100
tua
Hosta
A
2
alcula
eystro
2.4414
2.6130
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
2.7145
A=P(1+2)
yearly) (13)
squarterly) (143
(monthly) (13)
161 – 1
In graphi
alculators
the LNB
the numbe
2.7181
365
(daily)
8760
(hourly).
1(1)
ou must type
number before
pressing the LN key
b. Ir
>
You ca
logarit
Base e and Natural Logarithms In the table above, as n increases, the
expression 1(1 + 1)”) or (1 + 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
Куче
exponential functions are used extensively in
science to model quantities that grow and decay
continuously
12-15
EXAI
hy
3 Writ
a. e
(1, e)
e
(0, 1)
o
X
Most calculators have an e’ function for
evaluating natural base expressions.
ЗА. .
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