Skip to content

Commit

Permalink
versioning: chapter 5 is done!
Browse files Browse the repository at this point in the history
  • Loading branch information
@rhinopotamus
rhinopotamus committed Jul 26, 2024
1 parent 43dc0f0 commit e3e319f
Show file tree
Hide file tree
Showing 13 changed files with 984 additions and 826 deletions.
9 changes: 3 additions & 6 deletions source/textbook/ex-Approximation_and_rounding.ptx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -100,12 +100,9 @@
</task>
<task>
<statement>
<blockquote>
<p>
Hibbing [Minnesota] is the former boyhood home of Bob Dylan, basketball great Kevin McHale and the location of the Hull-Rust-Mahoning Open Pit Iron Mine, which has the largest iron-ore pit in the world. Hibbing is also the birthplace of [baseball star] Roger Maris.
<aside><p>(source: http://hibbing.areaconnect.com/)</p></aside>
</p>
</blockquote>
<p>
Hibbing, Minnesota is the hometown of baseball star Roger Maris, basketball great Kevin McHale, the Greyhound Bus lines, the Hull-Rust-Mahoning Open Pit Iron Mine and, perhaps most famously, songwriter Bob Dylan. It is not a big town.
</p>
<p>
In 2000 the population of Hibbing, Minnesota was reported at just over 17,000 residents. Based on a projected 0.4% decrease per year, the 2010 population was calculated to be <m>\mathbf{16,332.110\ldots}</m> people.
</p>
Expand Down
43 changes: 35 additions & 8 deletions source/textbook/ex-Exp_growth_decay.ptx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -205,11 +205,16 @@



<exercise xml:id="caffeine-growth-decay">
<exercise xml:id="caffeine-growth-decay" component="html">
<introduction>
<p>
Joe's girlfriend Ceyda starts the day by downing two cans of Red Bull, containing a total of 160 mg of caffeine. Her body eliminates the caffeine at a slightly slower rate of 12% each hour.
</p>
<p>
<em>
(Story also appears in <xref ref="caffeine-percentages"/>)
</em>
</p>
</introduction>
<task>
<statement>
Expand All @@ -236,11 +241,17 @@
</task>
</exercise>

<exercise xml:id="bacteria-growth-decay">
<exercise xml:id="bacteria-growth-decay" component="html">
<introduction>
<p>
The population of bacteria in a culture dish begins at 2,000 and will triple every day.
</p>
<p>
<em>
(Story also appears in
<xref ref="find-rate-growth-factor"/>)
</em>
</p>
</introduction>
<task>
<statement>
Expand Down Expand Up @@ -299,11 +310,16 @@
</task>
</exercise>

<exercise xml:id="house-value-growth-decay">
<exercise xml:id="house-value-growth-decay" component="html">
<introduction>
<p>
Tenzin bought a house for $291,900 but the housing market collapsed and his house value dropped 4.1% each year.
</p>
<p>
<em>
(Story also appears in <xref ref="house-value-percentages"/>)
</em>
</p>
</introduction>
<task>
<statement>
Expand All @@ -330,11 +346,17 @@
</task>
</exercise>

<exercise xml:id="wetlands-growth-decay">
<exercise xml:id="wetlands-growth-decay" component="html">
<introduction>
<p>
One modern technique for cleaning waste water involves the use of constructed (man-made) wetlands. Wetlands act as a natural biofilter for various contaminants in the waste water. After each month in the wetlands, only about of the contaminants remain in any given sample. Suppose a sample had 8 grams of contaminants before processed in the constructed wetlands.
</p>
<p>
<em>
(Story also appears in
<xref ref="find-rate-growth-factor"/>)
</em>
</p>
</introduction>
<task>
<statement>
Expand Down Expand Up @@ -377,13 +399,13 @@
</task>
</exercise>

<exercise xml:id="hibbing-growth-decay">
<exercise xml:id="hibbing-growth-decay" component="html">
<introduction>
<p>
Hibbing, Minnesota is the hometown of baseball star Roger Maris, basketball great Kevin McHale, the Greyhound Bus lines, the Hull-Rust-Mahoning Open Pit Iron Mine and, perhaps most famously, the childhood home of songwriter Bob Dylan. It is not a big town. In 2000 the population was reported at 17,071 residents, with an expected decrease of around 0.4% per year.
Hibbing, Minnesota is the hometown of baseball star Roger Maris, basketball great Kevin McHale, the Greyhound Bus lines, the Hull-Rust-Mahoning Open Pit Iron Mine and, perhaps most famously, songwriter Bob Dylan. It is not a big town. In 2000 the population was reported at 17,071 residents, with an expected decrease of around 0.4% per year.
</p>
<p>
<em>(Story also appears in ...)</em>
<em>(Story also appears in <xref ref="round-calculated-approx-rounding"/>)</em>
</p>
</introduction>
<task>
Expand Down Expand Up @@ -419,11 +441,16 @@
</task>
</exercise>

<exercise xml:id="food-shelf-growth-decay">
<exercise xml:id="food-shelf-growth-decay" component="html">
<introduction>
<p>
Donations to a local food shelf have increased 35% over last year. There were 3,400 pounds of food donated last year. <em>Story also appears in 5.3 #4</em>
</p>
<p>
<em>
(Story also appears in <xref ref="find-growth-factor"/>)
</em>
</p>
</introduction>
<task>
<statement>
Expand Down
93 changes: 52 additions & 41 deletions source/textbook/ex-Growth_factor.ptx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -7,33 +7,36 @@
<xi:include href="ex-intro.ptx" />

<page>
<introduction>
<p>
<term>Percent Change Formula:</term>
</p>

<p><ul>
<li>
<p>
If a quantity changes by a percentage corresponding to growth rate <m>r</m>, then the growth factor is <me>\displaystyle g=1+r</me>
</p>
</li>

<li>
<p>
If the growth factor is <m>g</m>, then the growth rate is <me>r = g-1</me>
</p>
</li>

</ul></p>

<p>
<term>Growth Factor Formula:</term>
</p>

<p>
If a quantity is growing (decaying) exponentially, then the growth (decay) factor is <me>\displaystyle g = \sqrt[t]{\frac{a}{s}}</me> where <m>s</m> is the starting amount and <m>a</m> is the amount after <m>t</m> time periods.
</p>
<introduction component="print">
<assemblage xml:id="growth-factor-formula">
<title>Growth Factor Formula</title>


<p>
If a quantity is growing (or decaying) exponentially, then the growth (or decay) factor is <me>\displaystyle g = \sqrt[t]{\frac{a}{s}}</me> where <m>s</m> is the starting amount and <m>a</m> is the amount after <m>t</m> time periods.
</p>
</assemblage>


<assemblage xml:id="percent-change-formula-2">
<title>Percent Change Formula</title>


<p>
<ul>
<li>
<p>
If a quantity changes by a percentage corresponding to growth rate <m>r</m>, then the growth factor is <me>\displaystyle g=1+r</me>
</p>
</li>
<li>
<p>
If the growth factor is <m>g</m>, then the growth rate is <me>r = g-1</me>
</p>
</li>
</ul>
</p>
</assemblage>
</introduction>
</page>

Expand Down Expand Up @@ -83,7 +86,7 @@
<task>
<statement>
<p>
Use the <term>Growth Factor Formula</term> to find the annual growth factor for the time period from 1962 to 1970.
Use the <xref ref="growth-factor-formula" text="title"/> to find the annual growth factor for the time period from 1962 to 1970.
</p>
</statement>
</task>
Expand Down Expand Up @@ -227,7 +230,8 @@
</p>

<p>
<em>Hint: First decide if you can use the <term>Percent Change Formula</term> or if you will need to use the <term>Growth Factor Formula</term>.</em>
<em>Hint: First decide if you can use the <xref ref="percent-change-formula-2" text="title"/> or if you will need to use the <xref ref="growth-factor-formula" text="title"/>.</em>

</p>

<p>
Expand Down Expand Up @@ -442,7 +446,9 @@
<task xml:id="reality-tv-growth-factor">
<statement>
<p>
The number of households watching reality television <m>R</m> (in millions) was estimated by the equation <me>R=2.5 \ast 1.072^T</me> where <m>T</m> is the time in years since 1990. <em>(Story also appears in 5.1 Exercises)</em>
The number of households watching reality television <m>R</m> (in millions) was estimated by the equation <me>R=2.5 \ast 1.072^T</me> where <m>T</m> is the time in years since 1990.
<em component="html">(Story also appears in <xref ref="reality-tv-modeling-exponential"/>)</em>
<em component="print">(Story also appears in <xref ref="sec-Modeling_exponential_equations"/> Exercises)</em>
</p>
</statement>
</task>
Expand All @@ -453,10 +459,14 @@
</p>
</statement>
</task>
<task xml:id="angry-birds-growth-factor">
<task xml:id="drawing-game-growth-factor">
<statement>
<p>
The number of players of a wildly popular mobile app drawing game has been growing exponentially according to the equation <me>N = 2 \ast 1.57^W</me> where <m>N</m> is the number of players (in millions) and <m>T</m> is the time in weeks since people started playing the game. <em>(Story also appears in 5.1 Exercises)</em>
The number of players of a wildly popular mobile app drawing game has been growing exponentially according to the equation <me>N = 2 \ast 1.57^W</me> where <m>N</m> is the number of players (in millions) and <m>T</m> is the time in weeks since people started playing the game.
<em>(Story also appears in
<xref ref="drawing-game-modeling-exponential"/>)</em>
<em>(Story also appears in
<xref ref="sec-Modeling_exponential_equations"/> Exercises)</em>
</p>
</statement>
</task>
Expand All @@ -465,7 +475,7 @@



<exercise xml:id="childhood-obesity-growth-factor">
<exercise xml:id="childhood-obesity-growth-factor" component="html">
<introduction>
<p>
Estimates for childhood obesity for 2010 were revised to 2.1 out of every ten children. (The 1994 figure of 1.1 out of every ten children remains accurate.)
Expand Down Expand Up @@ -504,7 +514,7 @@
</task>
</exercise>

<exercise xml:id="find-rate-growth-factor">
<exercise xml:id="find-rate-growth-factor" component="html">
<introduction>
<p>
For each equation, find the growth rate (percent increase or percent decrease) and state the units. (For example, something might <q>grow 2% per year</q> while something else might <q>drop 7% per hour</q>)
Expand All @@ -513,29 +523,30 @@
<task>
<statement>
<p>
The light <m>L\%</m> that passes through panes of glass <m>W</m> inches thick is given by the equation <me>L = 100\ast 0.75^W</me> <em>Story also appears in <xref ref="window-glass-approx-solutions"/> and <xref ref="window-glass-solving-exponential"/></em>
The light <m>L\%</m> that passes through panes of glass <m>W</m> inches thick is given by the equation <me>L = 100\ast 0.75^W</me>
<em>(Story also appears in <xref ref="window-glass-approx-solutions"/> and <xref ref="window-glass-solving-exponential"/>)</em>
</p>
</statement>
</task>

<task>
<statement>
<p>
The population of bacteria (<m>B</m>) in a culture dish after <m>D</m> days is given by the equation <me>B=2,000\ast 3^D</me> <em>Story also appears in <xref ref="bacteria-growth-decay"/></em>
The population of bacteria (<m>B</m>) in a culture dish after <m>D</m> days is given by the equation <me>B=2,000\ast 3^D</me> <em>(Story also appears in <xref ref="bacteria-growth-decay"/>)</em>
</p>
</statement>
</task>

<task>
<statement>
<p>
The remaining contaminants (<m>C</m> grams) in a waste water sample after <m>M</m> months of treatment is given by <me>C=8 \ast 0.25^M</me> <em>Story also appears in <xref ref="wetlands-growth-decay"/></em>
The remaining contaminants (<m>C</m> grams) in a waste water sample after <m>M</m> months of treatment is given by <me>C=8 \ast 0.25^M</me> <em>(Story also appears in <xref ref="wetlands-growth-decay"/>)</em>
</p>
</statement>
</task>
</exercise>

<exercise xml:id="antique-table-growth-decay">
<exercise xml:id="antique-table-growth-factor" component="html">
<introduction>
<p>
Years ago, Whitney bought an antique mahogany table worth $560. Now, 30 years later, she had the table appraised for $3,700.
Expand All @@ -558,7 +569,7 @@
</task>
</exercise>

<exercise xml:id="morphine-growth-decay">
<exercise xml:id="morphine-growth-factor" component="html">
<introduction>
<p>
The opiate drug morphine leaves the body quickly. After 72 hours about 10% remains. A patient receives 100 mg of morphine.
Expand Down Expand Up @@ -621,7 +632,7 @@
</task>
</exercise>

<exercise xml:id="unemployment-growth-factor">
<exercise xml:id="unemployment-growth-factor" component="html">
<introduction>
<p>
Unemployment figures were just released. At last report there were 20,517 unemployed adults and now, 10 months later, we have 39,061 unemployed adults.
Expand Down Expand Up @@ -660,7 +671,7 @@
</task>
</exercise>

<exercise xml:id="wetlands-acreage-growth-factor">
<exercise xml:id="wetlands-acreage-growth-factor" component="html">
<introduction>
<p>
Wetlands help support fish populations, various plant and animal populations, control floods and erosion from nearby lakes and streams, filter water, and help preserve our supply of ground water. Minnesota wetlands acreage in 1850 was 18.6 million acres. By 2003, that number had dropped to 9.3 million acres.
Expand Down
Loading

0 comments on commit e3e319f

Please sign in to comment.