Calculus - Standalone book
Calculus - Standalone book
3rd Edition
ISBN: 9781464125263
Author: Jon Rogawski, Colin Adams
Publisher: W.H. Freeman & Co
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Concept explainers

Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 7.6, Problem 17E
To determine

(a)

To find:

The balance in the annuity after 10 years and the time at which the annuity runs out of funds.

To determine

(b)

To show:

a continuous annuity with given withdrawal rate and interest rate funded by an initial deposit never runs out of money.

To determine

(c)

To find:

The minimum initial deposits P0 that will allow an annuity indefinitely.

To determine

(d)

To find:

The minimum initial deposits P0 necessary to fund an annuity for 20 years.

To determine

(e)

To find:

The minimum rate of interest r that the annuity must allow withdrawal to continue indefinitely.

To determine

(f)

To show:

a continuous annuity never returns outs of money if the initial balance is equal to or greater than Nr.

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Chapter 7 Solutions

Calculus - Standalone book

Ch. 7.1 - Prob. 1PQCh. 7.1 - Prob. 2PQCh. 7.1 - Prob. 3PQCh. 7.1 - Prob. 4PQCh. 7.1 - Prob. 5PQCh. 7.1 - Prob. 6PQCh. 7.1 - Prob. 7PQCh. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3E
Ch. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - Prob. 70ECh. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Prob. 77ECh. 7.1 - Prob. 78ECh. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - Prob. 81ECh. 7.1 - Prob. 82ECh. 7.1 - Prob. 83ECh. 7.1 - Prob. 84ECh. 7.1 - Prob. 85ECh. 7.1 - Prob. 86ECh. 7.1 - Prob. 87ECh. 7.1 - Prob. 88ECh. 7.1 - Prob. 89ECh. 7.1 - Prob. 90ECh. 7.1 - Prob. 91ECh. 7.1 - Prob. 92ECh. 7.1 - Prob. 93ECh. 7.1 - Prob. 94ECh. 7.1 - Prob. 95ECh. 7.1 - Prob. 96ECh. 7.1 - Prob. 97ECh. 7.1 - Prob. 98ECh. 7.1 - Prob. 99ECh. 7.2 - Prob. 1PQCh. 7.2 - Prob. 2PQCh. 7.2 - Prob. 3PQCh. 7.2 - Prob. 4PQCh. 7.2 - Prob. 5PQCh. 7.2 - Prob. 6PQCh. 7.2 - Prob. 7PQCh. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - 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Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - 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Prob. 112ECh. 7.3 - Prob. 113ECh. 7.3 - Prob. 114ECh. 7.3 - Prob. 115ECh. 7.3 - Prob. 116ECh. 7.3 - Prob. 117ECh. 7.3 - Prob. 118ECh. 7.3 - Prob. 119ECh. 7.3 - Prob. 120ECh. 7.3 - Prob. 122ECh. 7.4 - Prob. 1PQCh. 7.4 - Prob. 2PQCh. 7.4 - Prob. 3PQCh. 7.4 - Prob. 4PQCh. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.5 - Prob. 1PQCh. 7.5 - Prob. 2PQCh. 7.5 - Prob. 3PQCh. 7.5 - Prob. 4PQCh. 7.5 - Prob. 5PQCh. 7.5 - Prob. 1ECh. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Prob. 24ECh. 7.5 - Prob. 25ECh. 7.5 - Prob. 26ECh. 7.5 - Prob. 27ECh. 7.5 - Prob. 28ECh. 7.5 - Prob. 29ECh. 7.6 - Prob. 1PQCh. 7.6 - Prob. 2PQCh. 7.6 - Prob. 3PQCh. 7.6 - Prob. 4PQCh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - Prob. 7ECh. 7.6 - Prob. 8ECh. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - Prob. 20ECh. 7.6 - Prob. 21ECh. 7.6 - Prob. 22ECh. 7.6 - Prob. 23ECh. 7.6 - Prob. 24ECh. 7.7 - Prob. 1PQCh. 7.7 - Prob. 2PQCh. 7.7 - Prob. 1ECh. 7.7 - Prob. 2ECh. 7.7 - Prob. 3ECh. 7.7 - Prob. 4ECh. 7.7 - Prob. 5ECh. 7.7 - Prob. 6ECh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Prob. 9ECh. 7.7 - Prob. 10ECh. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Prob. 14ECh. 7.7 - Prob. 15ECh. 7.7 - Prob. 16ECh. 7.7 - Prob. 17ECh. 7.7 - Prob. 18ECh. 7.7 - Prob. 19ECh. 7.7 - Prob. 20ECh. 7.7 - Prob. 21ECh. 7.7 - Prob. 22ECh. 7.7 - Prob. 23ECh. 7.7 - Prob. 24ECh. 7.7 - Prob. 25ECh. 7.7 - Prob. 26ECh. 7.7 - Prob. 27ECh. 7.7 - Prob. 28ECh. 7.7 - Prob. 29ECh. 7.7 - Prob. 30ECh. 7.7 - Prob. 31ECh. 7.7 - Prob. 32ECh. 7.7 - Prob. 33ECh. 7.7 - Prob. 34ECh. 7.7 - Prob. 35ECh. 7.7 - Prob. 36ECh. 7.7 - Prob. 37ECh. 7.7 - Prob. 38ECh. 7.7 - Prob. 39ECh. 7.7 - Prob. 40ECh. 7.7 - Prob. 41ECh. 7.7 - Prob. 42ECh. 7.7 - Prob. 43ECh. 7.7 - Prob. 44ECh. 7.7 - Prob. 45ECh. 7.7 - Prob. 46ECh. 7.7 - Prob. 47ECh. 7.7 - Prob. 48ECh. 7.7 - Prob. 49ECh. 7.7 - Prob. 50ECh. 7.7 - Prob. 51ECh. 7.7 - Prob. 52ECh. 7.7 - Prob. 53ECh. 7.7 - Prob. 54ECh. 7.7 - Prob. 55ECh. 7.7 - Prob. 56ECh. 7.7 - Prob. 57ECh. 7.7 - Prob. 58ECh. 7.7 - Prob. 59ECh. 7.7 - Prob. 60ECh. 7.7 - Prob. 61ECh. 7.7 - Prob. 62ECh. 7.7 - Prob. 63ECh. 7.7 - Prob. 64ECh. 7.7 - Prob. 65ECh. 7.7 - Prob. 66ECh. 7.7 - Prob. 67ECh. 7.7 - Prob. 68ECh. 7.7 - Prob. 69ECh. 7.7 - Prob. 70ECh. 7.7 - Prob. 71ECh. 7.7 - Prob. 72ECh. 7.7 - Prob. 73ECh. 7.7 - Prob. 74ECh. 7.7 - Prob. 75ECh. 7.7 - Prob. 76ECh. 7.7 - Prob. 77ECh. 7.7 - Prob. 78ECh. 7.8 - Prob. 1PQCh. 7.8 - Prob. 2PQCh. 7.8 - Prob. 3PQCh. 7.8 - Prob. 4PQCh. 7.8 - Prob. 5PQCh. 7.8 - Prob. 1ECh. 7.8 - Prob. 2ECh. 7.8 - Prob. 3ECh. 7.8 - Prob. 4ECh. 7.8 - Prob. 5ECh. 7.8 - Prob. 6ECh. 7.8 - Prob. 7ECh. 7.8 - Prob. 8ECh. 7.8 - Prob. 9ECh. 7.8 - Prob. 10ECh. 7.8 - Prob. 11ECh. 7.8 - Prob. 12ECh. 7.8 - Prob. 13ECh. 7.8 - Prob. 14ECh. 7.8 - Prob. 15ECh. 7.8 - Prob. 16ECh. 7.8 - 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Prob. 56ECh. 7.9 - Prob. 57ECh. 7.9 - Prob. 58ECh. 7.9 - Prob. 59ECh. 7.9 - Prob. 60ECh. 7.9 - Prob. 61ECh. 7.9 - Prob. 62ECh. 7.9 - Prob. 63ECh. 7.9 - Prob. 64ECh. 7.9 - Prob. 65ECh. 7.9 - Prob. 66ECh. 7.9 - Prob. 67ECh. 7.9 - Prob. 68ECh. 7.9 - Prob. 69ECh. 7.9 - Prob. 70ECh. 7.9 - Prob. 71ECh. 7.9 - Prob. 72ECh. 7.9 - Prob. 73ECh. 7.9 - Prob. 74ECh. 7.9 - Prob. 75ECh. 7 - Prob. 1CRECh. 7 - Prob. 2CRECh. 7 - Prob. 3CRECh. 7 - Prob. 4CRECh. 7 - Prob. 5CRECh. 7 - Prob. 6CRECh. 7 - Prob. 7CRECh. 7 - Prob. 8CRECh. 7 - Prob. 9CRECh. 7 - Prob. 10CRECh. 7 - Prob. 11CRECh. 7 - Prob. 12CRECh. 7 - Prob. 13CRECh. 7 - Prob. 14CRECh. 7 - Prob. 15CRECh. 7 - Prob. 16CRECh. 7 - Prob. 17CRECh. 7 - Prob. 18CRECh. 7 - Prob. 19CRECh. 7 - Prob. 20CRECh. 7 - Prob. 21CRECh. 7 - Prob. 22CRECh. 7 - Prob. 23CRECh. 7 - Prob. 24CRECh. 7 - Prob. 25CRECh. 7 - Prob. 26CRECh. 7 - Prob. 27CRECh. 7 - Prob. 28CRECh. 7 - Prob. 29CRECh. 7 - Prob. 30CRECh. 7 - Prob. 31CRECh. 7 - Prob. 32CRECh. 7 - Prob. 33CRECh. 7 - Prob. 34CRECh. 7 - Prob. 35CRECh. 7 - Prob. 36CRECh. 7 - Prob. 37CRECh. 7 - Prob. 38CRECh. 7 - Prob. 39CRECh. 7 - Prob. 40CRECh. 7 - Prob. 41CRECh. 7 - Prob. 42CRECh. 7 - Prob. 43CRECh. 7 - Prob. 44CRECh. 7 - Prob. 45CRECh. 7 - Prob. 46CRECh. 7 - Prob. 47CRECh. 7 - Prob. 48CRECh. 7 - Prob. 49CRECh. 7 - Prob. 50CRECh. 7 - Prob. 51CRECh. 7 - Prob. 52CRECh. 7 - Prob. 53CRECh. 7 - Prob. 54CRECh. 7 - Prob. 55CRECh. 7 - Prob. 56CRECh. 7 - Prob. 57CRECh. 7 - Prob. 58CRECh. 7 - Prob. 59CRECh. 7 - Prob. 60CRECh. 7 - Prob. 61CRECh. 7 - Prob. 62CRECh. 7 - Prob. 63CRECh. 7 - Prob. 64CRECh. 7 - Prob. 65CRECh. 7 - Prob. 66CRECh. 7 - Prob. 67CRECh. 7 - Prob. 68CRECh. 7 - Prob. 69CRECh. 7 - Prob. 70CRECh. 7 - Prob. 71CRECh. 7 - Prob. 72CRECh. 7 - Prob. 73CRECh. 7 - Prob. 74CRECh. 7 - Prob. 75CRECh. 7 - Prob. 76CRECh. 7 - Prob. 77CRECh. 7 - Prob. 78CRECh. 7 - Prob. 79CRECh. 7 - Prob. 80CRECh. 7 - Prob. 81CRECh. 7 - Prob. 82CRECh. 7 - Prob. 83CRECh. 7 - Prob. 84CRECh. 7 - Prob. 85CRECh. 7 - Prob. 86CRECh. 7 - Prob. 87CRECh. 7 - Prob. 88CRECh. 7 - Prob. 89CRECh. 7 - Prob. 90CRECh. 7 - Prob. 91CRECh. 7 - Prob. 92CRECh. 7 - Prob. 93CRECh. 7 - Prob. 94CRECh. 7 - Prob. 95CRECh. 7 - Prob. 96CRECh. 7 - Prob. 97CRECh. 7 - Prob. 98CRECh. 7 - Prob. 99CRECh. 7 - Prob. 100CRECh. 7 - Prob. 101CRECh. 7 - Prob. 102CRECh. 7 - Prob. 103CRECh. 7 - Prob. 104CRECh. 7 - Prob. 105CRECh. 7 - Prob. 106CRECh. 7 - Prob. 107CRECh. 7 - Prob. 108CRECh. 7 - Prob. 109CRECh. 7 - Prob. 110CRECh. 7 - Prob. 111CRECh. 7 - Prob. 112CRECh. 7 - Prob. 113CRECh. 7 - Prob. 114CRECh. 7 - Prob. 115CRECh. 7 - Prob. 116CRECh. 7 - Prob. 117CRECh. 7 - Prob. 118CRECh. 7 - Prob. 119CRECh. 7 - Prob. 120CRECh. 7 - Prob. 121CRECh. 7 - Prob. 122CRECh. 7 - Prob. 123CRECh. 7 - Prob. 124CRECh. 7 - Prob. 125CRECh. 7 - Prob. 126CRECh. 7 - Prob. 127CRECh. 7 - Prob. 128CRECh. 7 - Prob. 129CRECh. 7 - Prob. 130CRECh. 7 - Prob. 132CRECh. 7 - Prob. 133CRE
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