Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

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Question

Chapter 7.4, Problem 45E

To determine

To calculate: annual rate of interest, compounded continuously for 100 years.

Expert Solution

Answer to Problem 45E

annual rate of interest =4.5% .

Explanation of Solution

Given information: What annual rate of interest, compounded continuously for 100 years, would have multiplied Benjamin Franklin’s original capital by 90 .

Formula used: The amount of money in the account after t year is then

A(t)=A0ert

Interest paid according to this formula is said to be compounded continuously. The number r is the continuous Interest rate.

Calculation:

The amount of money in the account after t year is then

A(t)=A0ert

Given

A0=1000,A(t)=90000,t=100 Years

A(t)=A0ert90000=1000e100re100r=90r=ln90100r=0.045r=4.5%

To determine

To calculate: annual rate of interest, compounded continuously for 100 years.

Expert Solution

Answer to Problem 45E

annual rate of interest =4.9% .

Explanation of Solution

Given information: Benjamin Franklin’s estimate that the original 1000 pounds would grow to 131000 in 100 years.

Formula used: The amount of money in the account after t year is then

A(t)=A0ert .

Interest paid according to this formula is said to be compounded continuously. The number r is the continuous Interest rate.

Calculation:

The amount of money in the account after t year is then

A(t)=A0ert

Given

A0=1000,A(t)=131000,t=100 YearsA(t)=A0ert131000=1000e100re100r=131r=ln131100r=0.049r=4.9%

Chapter 7.4, Problem 44E

Chapter 7.4, Problem 46E

Chapter 7 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 7.1 - Prob. 1QR Ch. 7.1 - Prob. 2QR Ch. 7.1 - Prob. 3QR Ch. 7.1 - Prob. 4QR Ch. 7.1 - Prob. 5QR Ch. 7.1 - Prob. 6QR Ch. 7.1 - Prob. 7QR Ch. 7.1 - Prob. 8QR Ch. 7.1 - Prob. 9QR Ch. 7.1 - Prob. 10QR

Ch. 7.1 - Prob. 11QR Ch. 7.1 - Prob. 12QR Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - 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