Exponential Functions Base e Investigations: 1. Thought Experiment: Suppose that you find a bank that pays 100% interest. You decide to invest $1.00 for one year. (a) Model this situation in terms of n, the number of compounding periods in a year. A= auout P= prinipal (intiul amount) Y= annual witerust rate n=c ompaunding peri ods per year tinumber Byears (b) If the bank is willing to compound your interest as often as you specify, what so you think is the most money you can make?

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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can you help me with number 1b

Exponential Functions Base e
Investigations:
1. Thought Experiment: Suppose that you find a bank that pays 100% interest. You decide to
invest $1.00 for one year.
(a) Model this situation in terms of n, the number of compounding periods in a year.
A= auout
P= prinipal lintial amouat)
r= annual unterest rate
t=number Biyears
n=compaunding seriods per year
(b) If the bank is willing to compound your interest as often as you specify, what so you
think is the most money you can make?
(c) Fill in the table to see how much money you could make. Round answers to six decimal
places.
numbei q times
the inaterest
c ompounded, th
humber gefs
Closer fo
infiniey
Interest compounded
Number of compounding
periods per year
A =1(1++)*"
annually
1
semi-annually
quarterly
2.25
4
2.4414
2.66130
217146
2,718,1
2.718.3
monthly
12
daily
hourly
365.24=8760
8760mino60=Sa$.600min
by the minute
by the second
continuously!!!!
Infinite
What number is A getting close to?
e =2,71878 constant /1t
Euler's
Generalization: This table shows that for large values of n, (1++)" = 2.7183
an irrational no! infindy
nunber
times ]
inmeusurcable
tiñnes a
ayear
year
Transcribed Image Text:Exponential Functions Base e Investigations: 1. Thought Experiment: Suppose that you find a bank that pays 100% interest. You decide to invest $1.00 for one year. (a) Model this situation in terms of n, the number of compounding periods in a year. A= auout P= prinipal lintial amouat) r= annual unterest rate t=number Biyears n=compaunding seriods per year (b) If the bank is willing to compound your interest as often as you specify, what so you think is the most money you can make? (c) Fill in the table to see how much money you could make. Round answers to six decimal places. numbei q times the inaterest c ompounded, th humber gefs Closer fo infiniey Interest compounded Number of compounding periods per year A =1(1++)*" annually 1 semi-annually quarterly 2.25 4 2.4414 2.66130 217146 2,718,1 2.718.3 monthly 12 daily hourly 365.24=8760 8760mino60=Sa$.600min by the minute by the second continuously!!!! Infinite What number is A getting close to? e =2,71878 constant /1t Euler's Generalization: This table shows that for large values of n, (1++)" = 2.7183 an irrational no! infindy nunber times ] inmeusurcable tiñnes a ayear year
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