Building Quadratic Functions (Part 2): IM Alg1.6.6
[url=https://im.kendallhunt.com/HS/teachers/1/6/6/preparation.html]“Building Quadratic Functions to Describe Situations (Part 2)”[/url] from IM Algebra I © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg1.6.6 Lesson
- IM Alg1.6.6 Lesson: Building Quadratic Functions to Describe Situations (Part 2)
- Alg1.6.6 Practice
- IM Alg1.6.6 Practice: Building Quadratic Functions to Describe Situations (Part 2)
IM Alg1.6.6 Lesson: Building Quadratic Functions to Describe Situations (Part 2)
A cannon is 10 feet off the ground. It launches a cannonball straight up with a velocity of 406 feet per second.
[size=150]Imagine that there is no gravity and that the cannonball continues to travel upward with the same velocity.[/size]
Complete the table with the heights of the cannonball at different times.
Write an equation to model the distance in feet, [math]d[/math], of the ball [math]t[/math] seconds after it was fired from the cannon if there was no gravity.[br]
Earlier, you completed a table that represents the height of a cannonball, in feet, as a function of time, in seconds, if there was no gravity.
[size=150]This table shows the actual heights of the ball at different times.[/size][br][center][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAiQAAACJCAYAAAAc7iNpAAAQw0lEQVR4nO2d3ZGruhJGqTqvNwEiIRMyIYWdgmNxLqQxz7oP+7SP3CPxYwNNq9eqUtWUzQAf0N2fJQFdAgAAADCms94BAAAAAAwJAAAAmIMhAQAAAHMwJAAAAGAOhgQAAADMwZAAAACAOZsMyf/+6Wg02hft5+eHRqPRaD8/3xsSAPgMD/GzlCQ8gQ6/oDkGGBIAQzzETyuJER1+QXMMMCQAhniIn1YSIzr8guYYYEgADPEQP60kRnT4Bc0xwJAAGOIhflpJjOjwC5pjgCEBMMRD/LSSGNHhFzTHAEMCYIiH+GklMaLDL2iOAYYEwBAP8dNKYkSHX9AcAwwJgCEe4qeVxIgOv6A5BhgSAEM8xE8riREdfkFzDDAkAIZ4iJ9WEiM6/ILmGGBIAAzxED+tJEZ0+AXNMcCQABjiIX5aSYzo8AuaY4AhATDEQ/y0khjR4Rc0xwBDAmCIh/hpJTGiwy9ojgGGBMAQD/HTSmJEh1/QHAMMCYAhHuKnlcSIDr+gOQYYEgBDPMRPK4kRHX5BcwwwJACGeIifVhIjOvyC5hhgSAAM8RA/rSRGdPgFzTHAkAAY4iF+WkmM6PALmmOAIQEwxEP8tJIY0eEXNMcAQ7KTvu9T13VpHEfrXYEG8BA/rSRGdPgFzTHAkOwEQwJHcmT8PB6P1HXdqz2fz0PWe3ZinKYpdV2X+r4/dTtn6Zjn+e24d12X5nk+ZVspXV+otLajrqs9WBbnYRhOP6clrtas84dFncOQ7ARDAkdyVPw8n8+3YiFF/ogkemZiHMcxjeOYpmlya0iGYXgr0uM4pq47Ly9eWagej8ebtiOvqz1YGZJpml7ns3XNotUSM0NS+lWRIxe+tMfj8WsdYg5Kyyy5enGCfd//2o5G3HHXdWkYhqIhkQtW2jRNHx0TiMdRhmQYhl/JRK7vb7kiMXo2JBrJbaWcdQSWvQWi7epeEgvNYvJFc+uGZBiG067ZrZgZEm0Y+r5/nXBd4LXhKJkZuWBq3+VGQS60UhuG4bWPuRmpdWVpQ4MhgT0cZUhKBXAcx7fr+VMwJPs4u2hbD1+cfZ5KWGiWcxjFkOgf+HcbmjvNkOSGQJ/k0ndS9CW55oZF/39uImqf5dsQ85Abi3mei8vkn4khkXVbd3WBT44wJLUCeFSRx5DsQ3LJWVxdqEq58GosegtEaxRDkuuTa/jqHpPb9JDIwShNrNFDKkvzOEqTcfJ1arMh29Wf5QYlR29b95BgTGAPGJK/tGJIzh6uScm2hyTCfIppmt56FqMYEs0wDIf0sO7BdFJrqYuoNASiDclS8V8zJM/n81BDotevh30AlmDI5i8tGBIpXGf3IlgXqr7vb3X3xdEs1Z8rdVuf5ytiUmNiSGSuhyBFfpqmxeEcIR+C+XbIpmZItg7ZlCbLntldC21xlCEpFQkmtb5zpo6rzEhK9oWqdUOioYfkOsznkJQm0dQmk8ovwNr/ayOx5f9rhmRpP0pzSOghgU84ypCIGfZ226/g2ZBcMUyTc/VtvzlyXUW4y0aIYEi0tjue59MMSWlYRgsv3Wmjf33UDEfpu3z9Ww1JSu/DSnJrZW5IMCPwDWc+GO2oBIohWebq7v0rC5UeVrcozClhSM6mVG8t4MFoAIZ4iB/rruOjQIdf0BwDDAmAIR7ip5XEiA6/oDkGGBIAQzzETyuJER1+QXMMMCQAhniIn1YSIzr8guYYYEgADPEQP60kRnT4Bc0xwJAAGOIhflpJjOjwC5pjgCEBMMRD/LSSGNHhFzTHAEMCYIiH+GklMaLDL2iOAYYEwBAP8dNKYkSHX9AcAwwJgCEe4qeVxIgOv6A5BhgSAEM8xE8riREdfkFzDDAkAIZ4iJ9WEiM6/ILmGGBIAAzxED+tJEZ0+AXNMcCQABjiIX5aSYzo8AuaY4AhATDEQ/y0khjR4Rc0xwBDAmCIh/hpJTGiwy9ojgGGBMAQD/HTSmJEh1/QHAMMCYAhHuKnlcSIDr+gOQYYEgBDPMRPK4kRHX5BcwwwJACGeIifVhIjOvyC5hhgSAAM8RA/rSRGdPgFzTE4xJDQaLTP2s/PD41Go9H+bV8bEgD4DA/xs5QkPIEOv6A5BhgSAEM8xE8riREdfkFzDDAkAIZ4iJ9WEiM6/ILmGGBIAAzxED+tJEZ0+AXNMcCQABjiIX5aSYzo8AuaY4AhATDEQ/y0khjR4Rc0xwBDAmCIh/hpJTGiwy9ojgGGBMAQD/HTSmJEh1/QHAMMCYAhHuKnlcSIDr+gOQYYEgBDPMRPK4kRHX5BcwwwJACGeIifVhIjOvyC5hhgSAAM8RA/rSRGdPgFzTHAkAAY4iF+WkmM6PALmmOAIQEwxEP8tJIY0eEXNMcAQwJgiIf4aSUxosMvaI4BhgTAEA/x00piRIdf0BwDDAmAIR7ip5XEiA6/oDkGGBIAQzzETyuJER1+QXMMbmVI+r5PXdelcRxTSilN05S6rkt93x+2DQ88n8/UdV3qui7N82y9O03xeDxudWwxJNeBDr+gOQa3NiTjOL6KxxZk2WmaDtsnCzAk54Eh2U8riREdfkFzDG5tSPaCIYE1MCT7aSUxosMvaI6BqSEZhuFVHIZh2DRkM8/z63/y3hP9Wdd16fl8ppTee1pKQ0Cy3bxY1YyNLCvt8Xi8vlvaRk5JQ76e3JDofRJNpWV1b1L+v/n6RUO+j/m5WCvWcl6kyfEdhuFtu8MwvP7Oj6XeVv5dfmxkn0ufbT1n+vjk1wKGZButJEZ0+AXNMTAzJLoo6aKRUtmQ6GX7vi8WeCnepYK9VoxLBqC2jXmeq9/VTElte1Jsa/us90kX49Iy2uTl+6qXKWnTaDNSOm+y//l6xSjUtiVmZqsh2XLO1o4jhmQbrSRGdPgFzTEwMSR5oZBClX9WMyRrQxm1X8n5sqV15MVNr6s0n0VvW/4/H2rSxbG2P6X/Lx2fvCjLcrqYlz7LDURK/5kYOaYl0yf7U+ohWjIQpf3Pj0m+L3Jc9GefGJLaOSstk3+GIdlGK4kRHX5BcwxMDIkuksKWIZulX7k1Q1L7pSxFsWQo9GdL81tqv/prRT1ff6mXoGa85H+GYfg1rCOIcZJjpntE5PuS0artj1DqXSkdq7X9rw3BPR6P3YZk6ZyVzgFzSPbTSmJEh1/QHAN3hiRfThfHtQL0jSEp/eIXauuvGZK1YYsjDEmpV2Capte2tfYthiTf5hmGZJomDMkNaSUxosMvaI6BqyEbma8hSHHV8xNKEyiX5lBsKW5LXf2l/9+iXdajJ4WuDdnIZyXjUPosH6bRhmDvs170+teGbPJjtWXIJt+GrK80OXfvOdPLYEi200piRIdf0BwDV5Natw695AVnaUhijyGpbXue500TZ4XaBNiaISk1YWmCqS62+Xe612brOlJaHuJZMyRL2yod+1LbY0iY1HoMrSRGdPgFzTEwve03H7oYhuHX/AZtSEoFOB860MVeCo7eTn7LaErbitvroFQKZM1olNDDSHreR37brDYAmqXbfnPWegZKw0ilCbkpvZuScRw3D9mU9qVkkPRxzrex95zpY82QzX5aSYzo8AuaY3CrB6PB/dHDZqX5HbAdD/HTSmJEh1/QHAMMCexiaZIw7Oeb+FnriVp7qN5WjkqMeS9gju7B3Pv9Vj7RsTTEmvfslXoYa48bsNAh7Jkztnb96B7rpSdkb91mjSs0r/U2Lw1X5xyVF7/R/MnTvrc8NPLTGN4KhgR2UTIk31yA0fk0fh6PR+r7/pV4dAKRz/Xk4U+GqY4wJDL8qJPZMAy/JmXrYbil7/dwlLEqHfOlY1tb/mod4zimcRxfd9stsXb96HXI8qVe0tq538MVmvX5kOH9JUSboI/BlnXU+FTzWm7QyHJrr1z5NIb3gCEBMOTb+KklHZ0oU/r7K+aT9zx9W8inaXq9RqBUxPJ9F8O75fu9HGVI9LF9Pp+LRadUDGVe1CcccT72FtqU3q+frddX7dzv5QrNmrVrTV+fd7tetxqSLct8GsN7wZAAGHKWISn9Wv20CB7RdZxS+pXMSkVChkiez+fq93s5wpAsJeBaj6Hss76F32oIbUtxXrt+RLN+jUXO0rnfi4UhWfulXzNl+fn/9EdAStcYkmma3m4aKF2/38TwXjAkAIacYUhqCeGTpJzSd4lRF618+zWDJMVw7fu9HDn0lFMyg2vj7N/c4XV2cd56/eTza0rrWzr3e7nKkJSei1RiqdjnczG+meh/hSHRD8pMKf0yJd/E8F4wJACGtGxIhmH49ZRcz4Zk75i8fsmj7LP0JljNhTnCkOg5JVKE89vyl879Xix6SPq+X3xBau2p3fohnFfPIRG2XK+luSNyfc7z/HUM7wVDAmBIq0M2aw+lezwe7oZsakWohC7O+v8s5xYcMWSz9P2Wc78XC0Mi15re31rM3e163dpDUnv3258/f76O4b1gSAAMOcuQ9H1/m0mtgv51lf8S059t+X4vR8yF2TLUontISse9pG0rVxTnpeunVnCW7qTx2ENSMyQ1Y1oy/LV1bOEKQ6LvkElpOcb2xvBeMCQAhpxlSPSkQ+vbfmWfSi/KXLplcO37PXyjY6l3pNQ7le+zDGfo93Dd6S4bPfF27frRwxn6/zV3NST5eSgZj9pE3aXn/pRedvoJZxmSXHPpdu295/GqGMWQAJzMWYYkpd93f3w6kfJMQ5LS+2TPUiJb+34rn+pYMnOlB6eVkrl+iJiFjnxf9HnI76QQ1q4f/QqIpV6AuxoSMV2l81hbfunc6eEqS81Lw7l575be56Ve1E9jeCumhkSCND8A+QzlMx+4Jdv+5uABfIsHQ9/KI6zRUUdu/7wrZ2hee36MNWh+53RDok3Hkb8icvL15ojDv8NL1iAmGJLrQEedTychXsUZmvUdJHcDze+cakhK421iEI7uGakZEtmHO58gaBsMyXWgwy9ojoGZIdG9E3o8Mnfseoyr1HOi/z9/54JerxgeGTfkXSxgBYbkOtDhFzTHwMyQyCQYoWZIam+X1TPxS8vM87xoSFL6782MABZgSK4DHX5BcwzMDElpBnJpyEbP4M57S1Iqv1pa1iNDMbUhm5R+GyOAK8GQXAc6/ILmGNzakJRuxdI9KPldObWekC2GhImtYAGG5DrQ4Rc0x+DWhmTtEcTP57M41POJIQGwAENyHejwC5pjcJs5JCltG7LRlIZsNPk8FA1zSMASDMl1oMMvaI7Bbe6yyT9bejZJaVJrrYdE1l27S4e7bMAaDMl1oMMvaI6BmSERo7HlOSSlO230MqU7bfIH/eRzTcSQ8BwSsAZDch3o8AuaY3CrJ7VeDU9qBWswJNeBDr+gOQa3e5fNVfAuG7gDGJLrQIdf0BwD3vYLYIiH+GklMaLDL2iOAYYEwBAP8dNKYkSHX9AcAwwJgCEe4qeVxIgOv6A5BhgSAEM8xE8riREdfkFzDDAkAIZ4iJ9WEiM6/ILmGGBIAAzxED+tJEZ0+AXNMcCQABjiIX5aSYzo8AuaY4AhATDEQ/y0khjR4Rc0xwBDAmCIh/hpJTGiwy9ojgGGBMAQD/HTSmJEh1/QHAMMCYAhHuKnlcSIDr+gOQYYEgBDPMRPK4kRHX5BcwwwJACGeIifVhIjOvyC5hhgSAAM8RA/rSRGdPgFzTHAkAAY4iF+WkmM6PALmmNwiCGh0WiftZ+fHxqNRqP9274yJAAAAABngiEBAAAAczAkAAAAYA6GBAAAAMzBkAAAAIA5/wd+GPlYict+uQAAAABJRU5ErkJggg==[/img][/center][br]Compare the values in this table with those in the table you completed earlier. Make at least 2 observations.
Plot the two sets of data you have on the same coordinate plane. Right click on a point to find the setting to change its color.
How are the two graphs alike? How are they different?[br]
Write an equation to model the actual distance [math]d[/math], in feet, of the ball [math]t[/math] seconds after it was fired from the cannon. If you get stuck, consider the differences in distances and the effects of gravity from a previous lesson.[br]
[size=150]The function defined by [math]d=50+312t-16t^2[/math] gives the height in feet of a cannonball [math]t[/math] seconds after the ball leaves the cannon.[/size][br][br][size=100]What do the terms 50, [math]312t[/math], and [math]-16t^2[/math] tell us about the cannonball?[/size][br]
Use graphing technology to graph the function. Adjust the graphing window to the following boundaries: 0 < x < 25 and 0 < y < 2,000.
Observe the graph and:
Describe the shape of the graph. What does it tell us about the movement of the cannonball?[br]
Estimate the maximum height the ball reaches. When does this happen?[br]
Estimate when the ball hits the ground.[br]
What domain is appropriate for this function? Explain your reasoning.[br]
If the cannonball were fired at 800 feet per second, would it reach a mile in height? Explain your reasoning.
IM Alg1.6.6 Practice: Building Quadratic Functions to Describe Situations (Part 2)
[size=150]The height of a diver above the water, is given by [math]h\left(t\right)=-5t^2+10t+3[/math], where [math]t[/math] is time measured in seconds and[/size][size=150] [math]h\left(t\right)[/math] is measured in meters. Select [b]all[/b] statements that are true about the situation.[/size]
[size=150]The height of a baseball, in feet, is modeled by the function [math]h[/math] given by the equation [math]h\left(t\right)=3+60t-16t^2[/math]. The graph of the function is shown.[/size][br][img]data:image/png;base64,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[/img][br]About when does the baseball reach its maximum height?
About how high is the maximum height of the baseball?
About when does the ball hit the ground?
[size=150]Two rocks are launched straight up in the air. The height of Rock A is given by the function [math]f[/math], where [math]f\left(t\right)=4+30t-16t^2[/math]. The height of Rock B is given by [math]g[/math], where [math]g\left(t\right)=5+20t-16t^2[/math]. In both functions, [math]t[/math] is time measured in seconds and height is measured in feet.[br][/size][br]Use graphing technology in the applet below to graph both equations. Determine which rock hits the ground first and explain how you know.
[size=100][size=150]Each expression represents an object’s distance from the ground in meters as a function of time, [math]t[/math], in seconds.[br][br]Object A: [math]-5t^2+25t+50[/math][br][br]Object B: [math]-5t^2+50t+25[/math][/size][/size][br][br]Which object was launched with the greatest vertical speed?
Which object was launched from the greatest height?
[size=150]Tyler is building a pen for his rabbit on the side of the garage. He needs to fence in three sides and wants to use 24 ft of fencing.[br][/size][br][img]data:image/png;base64,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[/img][br]The table below shows some possible lengths and widths. Complete each area.
Which length and width combination should Tyler choose to give his rabbit the most room?
Here is a pattern of dots.
[img]data:image/png;base64,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[/img]
How many dots will there be in Step 10?[br]
How many dots will there be in Step [math]n[/math]?
[size=150]The function [math]f[/math] is defined by [math]f\left(x\right)=2^x[/math] and the function [math]g[/math] is defined by [math]g\left(x\right)=x^2+16[/math].[/size][br][br]Find the values of [math]f[/math] and [math]g[/math] when [math]x[/math] is 4, 5, and 6.
Will the values of [math]f[/math] always be greater than the values of [math]g[/math]? Explain how you know.
[size=150]Han accidentally drops his water bottle from the balcony of his apartment building. The equation [math]d=32-5t^2[/math] gives the distance from the ground, [math]d[/math], in meters after [math]t[/math] seconds.[/size][br][br][size=100]Complete the table below and plot the data on the coordinate plane below.[/size][br]
Is the water bottle falling at a constant speed? Explain how you know.
The graph shows how much insulin, in micrograms (mcg), is in a patient's body after receiving an injection.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALQAAAC1CAYAAAD2kdWXAAAXjklEQVR4nO2dW2wbWRnHD9B22S6S/QgSyJa4rCgSYwQCiYvsF154wHmDFaDxC5cHkK1FrLQIafzEA9LiIJBAoGXSphvSpPU4iZO4SdpxN70kTZPJZR07JOmku0kvGzYTEsim5fLnIczs+JbMNHOSsef8pE9q3Ph8Y/vnyTdnzoWgSSgUChgfHzcim83i3LlzRnR2dmJoaMjRuHjxInK5nOPtmiOdTmNwcJBqjkwmg/7+fqo5ent70dfXRzVHX18fyHGL6BT/+te/8OTJEyO++93v4h//+IcROzs7ePz4saORy+WwtbXleLvmyOfzePvtt6nmGB8fx71796jmmJ2dxcLCAtUcf/3rX5tHaDOqqoIQAlVVqeYZHh7G7u4u1Ryjo6PQNI1qjsnJSdy/f59qjvn5eSwvL1PNcffu3eYUOpVKgRCCVCpFNQ8T2jpM6EPwqU99CoQQfPrTn6aahwltHSb0U6IoCgghRtAsO5jQ1nGd0KqqIp/P0zweR4jH43jf+95nCE2z7GBCW+fYhdY0Da2trYhEImVnPEII/H4/YrEYZFmmeoBPw4c//OGyY33++eep5WJCW+dYhVYUBX6/H9FoFKIoVv3ZlmUZ8XgcgUAAsViM6kHaQS83XnnlFRBC8Lvf/Y5q2cGEts6xCi1JEhRFsdSIIAhOHtOhiMfjEEURb731Fggh2NjYgCiK1MoOJrR1jr3kaET0EsgsNADLX067MKGt4wqhNU1DOBw2fpYkCX6/H4QQiKJI9eDs8s477+Dhw4d4+PAhpqamQAjB66+/junpaUxPT6NQKODNN990NNLpNJaXlx1v1xzZbBbz8/NUc4yMjEBRFKo5RkdHMTY2RjXH+Pj4/kLLslwmdCAQgCzL0DQNPp+PtqO2eOutt7C4uIjFxUWMjo6CEIJLly4Z9/mvXbuGmZkZR6OjowOTk5OOt2uO7u5u3Lp1i2qOnp4eKu+POQYHBzE8PEw1x8jIyMFC6zWyJEllcpv/7TYqSw5asJLDOq4oOVRVRSAQgKqqCIVCZWWG287QZpjQ9vCM0MBeL4bP50M8HjceUxQFHMdRPbjDwIS2h6eEbkSY0PbwnND6be/KcCtMaHt4SuhoNApCCMLhcFW4FSa0PTwjtCzLCAQC1N9Qp2FC28NTQvM873hiWZaRTCbR2tpa9WGlUikkk8mqu3v6c9ra2g5sP5fLgRCC6elpR4+7Eia0dVwhtKZp4DjO0TdUFEUIggBZliGKYllvCc/zSKVSkGUZHMcZt7IlSTJ+5nm+rMelEr1E0oPmHU0mtHVcITSwd8b0+/2IRCJV4QThcBiapkFV1TK5JUky/jpEo9GyM3a9L5ksy1VDXdlou4PxjNCqqsLv9yMej0MQhKo4LJqmIRAIANiTMRqNlv2/fuGp/4758cqx2KVSCT/4wQ/w7LPPlsn8zDPP4Ic//CHS6TRkWXY0Xn31VQwPDzverjnOnj2LwcFBqjk6OjrQ29tLNUdXVxeVz8Ac6XT64Bq6UjIn4XneKAlkWa76kuh3IwkpP8xaQu/u7uLChQs4efJkmdAnT55ET08PNE0rW9bAiRgYGMDGxobj7ZrjypUrWFtbo5rj5s2bWF5epppjamoKhUKBao75+fn9hVYUhVr3HM/zZRecco0LUDtnaGDvjP+xj33MOEs/++yzeOGFF5w9cBOs5LCOK0oOYE+8ZDKJfD7v2BtbKTOAqhra/NehsoberytR0zQIgmDMWKEJE9o6rhBarnORpcfTEI/HEQqFyu446hdt8Xgcra2tyOfzCIVCxllYH+mXz+eRTCb37eUAWD+0XTwjNA30bjtzmMuHVCpV9RjwXo1tZToVE9oeTGiXw4S2h6eEliSpZh+0U/3QNGBC28MzQquqCp/PZ8yc1rvZOI6DJElUD+4wMKHt4RmhzV1p5n5i8w0RN8KEtoenhNa7zir7idnwUSa0HVwhNFB+U4PjOGQyGWQyGdfNKdzc3MT6+jrW19cxMzMDQghu3bqF+fl5zM/PY2lpCffv33c0JEnCvXv3HG/XHAMDA1hYWKCa4+rVq5idnaWa48aNG5iYmKCa486dO/Z6OWR5b3x0IBBw3bocKysrKBaLKBaLRv95Z2cnstksstksRkZGcOfOHUejvb0dY2Njjrdrjs7OToyOjlLNkU6nceXKFao5stkscrkc1Ry5XO7gi0I3X/zVg5Uc9vBMySHLsqtr5Xowoe3hGaH13gzae5U4DRPaHp4SurW1FX6/H4lEAslksizcChPaHp4RWlXVmgP7nRrgTwsmtD08I3SjwoS2h2eErjWLREcf4xGLxVy3zAET2h6eEjoYDBprQpuHbvp8PkiSBEEQqE7TehqY0PbwlND6DGt98XNFUaq689w2roMJbQ9PCW0uOfSB95VCh8NhV3XtMaHt4RmhFUUpKyei0SgSiUTNxc+Pu45eXFw0tp+4fPkyCCH485//jK6uLnR1daG3txejo6OOhiiKyOfzjrdrjvb2dgwPD1PNceHCBQwMDFDNkU6n0dPTQzVHb2+vtcUag8EgQqEQOI4zxkNHo1G0trYik8m4ouT45z//ie3tbWxvb6NUKoEQgkKhgLW1NaytreHBgwdG6eRU9PX14dGjR463a46hoSHcu3ePao7R0VEsLCxQzTExMYGZmRmqOWZnZ6112+l1sxlN0xCNRo262k2wksMenik5KjnussIqTGh7eEpoVVWrtkdOJBKulpsJbQ9PCc1xHARBMN5UVVURjUYPXBvjOGFC28MzQu83fPRpF5o5CpjQ9vCU0PXuArqhZ6MeTGh7eEZoTdsbD13Zi1G5ULnbYELbwzNCA3vy+nw+Y3GZUChUU3I3wYS2h6eEBvbO1Ppt8FrL2LoNJrQ9PCO0oiiu7s0ws7W1hY2NDWxsbGBubg6EEExOTmJpaQlLS0tYWVnB22+/7Wj09PRgdXXV8XbNkcvlsLy8TDVHPp9HoVCgmmNsbAxTU1NUcyiKcnwLnjvN3bt3USgUUCgUcOXKFRBC8Nprr6Gnpwc9PT3I5XIYHx93NM6dO4cbN2443q45/vKXvyCfz1PNcenSJQwPD1PN0dvbi4GBAao5BgYGrC143traehROOgYrOezhqZJDv0tYaycst8KEtodnhNYvBuuFW2FC28MzQjcqTGh7eEZoRVFq3kDRb7i4FSa0PTwjNBvLsT9MaOu4RuhQKFT1uKZpTGgwoe3gCqGBveGjsVjM2Kcwn8+jpaXF1TdcmND28JTQqqqC53n4fD4QQhAIBMrGR7sRJrQ9PCV0I8KEtkfTC62qqqvPwLVYXl7G3Nwc5ubmMDw8DEII2tvbIUkSJElCf38/bt265WicPXsW169fd7xdc3R0dODq1atUc3R3d+Py5ctUc2QyGWSzWao5+vv7awsdDoeNkXVOb41Mi+3tbWxubmJzcxOFQgGEEExPT0NVVaiqitXVVfztb39zNHp7e3H//n3H2zXH5cuXoaoq1Ryvv/46isUi1Rzj4+NQFIVqjunpaVZyHAZWcliH1dCHgAltD08JLcsyEokE2xq5Bkxo67hCaFVV4ff7EY/H2Qr+NWBCW8cVQu8369vNMKHt4RmhG2nGihkmtD08IzSwt/poMplEPp+vCrfChLaHp4TmeZ5KP3Q8Hq/aXlmfIcNxHBKJRNXvcxyHlpaWAz9gJrQ9PCO0oigIBAKOvqGapiESiYDn+aoLS/N6HzzPG8ILgmDs72KlDGJC28MzQsuyDJ7nHU+sqmrVdheVopp/rtzyguO4qi0wdnZ2sLW1ha2tLRSLRRBC8MYbb2B1dRWrq6tUFjzPZrPUFzwfHh5mC55bjAMXPNc0zdg0yGkqhZZluWpIqj5bprK8CYfDVXMaFxcXMTMzg5mZGQwNDYEQgra2Nly8eBEXL15Eb28vrl+/7mi0tbXh2rVrjrdrjvPnz2NkZIRqjgsXLmBwcJBqjnQ6TeUzMEdfX9/B/dAtLS0IBoNoaWlxdGvkWkLXKkEAa0KbYSWHPTxTctDcGrmW0OaSQ9M04+fKeY1MaGfxjNA0qXdG1j88URSNEoTneUiSBMDaBF0mtD2aXmhRFC2tu6FpWlX3mlVqCa0v05tIJMq2itPP1olEAsFgsKq7rxImtD2aXmh9+YJQKGTcVNF7FWRZRltbG2KxGAghT116aJpWc7NOTdPqLtUry7KlD5cJbY+mF1pHkiREo1FjPqEeHMchHo+7avdYM0xoe3hG6EaFCW0PJrTLYULbgwntcppBaEVRcObMGaPMO2y//34woV1OMwj9kY98pOy65dSpU0bXpdMwoV3IysoKisUiisWiMVu9s7MT2WwW2WwWQ0NDmJiYcDTa29tx69Ytx9s9f/58zdGN3/72tx3PNTExgXQ6jZGRESpt69HX14fBwUGqOXK53MFCS5JUcz6h2+YUbm5uGtPZZ2dnQQjB+Pg4SqUSSqUSlpeX8eDBA0cjk8ng3r17jrdbKpWqZH7/+9+Pn/70p47nevDgAa5evYq5uTkqbetx8+ZNTExMUM1x586dg299E0KMGy1swfNyaJYc3/jGN/DBD34QhBCcOHECp0+fptZN6pmSg80p3B/avRypVApnzpzBCy+8QLXP3zNCszmF+8O67azjCqGBvZFtbW1tVA/EaZjQ9vCM0IqiIBgMNsTadmaY0PbwjNCaxnbB2g8mtHVcIXSjwoS2R9MLLQgCJEmCqqpV066cmoJFEya0PZpeaL3fmeYULJowoe3R9EI3Iru7u9jZ2cHOzg4WFxdBCMHi4iLW19exvr6Od955B9vb245Gf38/lXbNMTIygrW1Nao5bt68iaWlJao5pqam8MYbb1DNUSgUqoXe2dmBoigHxszMzHF4W5dSqYTJyUlMTk5iYGAAhBD88Y9/REdHBzo6OnDp0qV9L3CfJl599VWMjIw43q45zp49i8HBQao5Ojo60NfXRzVHd3c30uk01RySJFULPTs7i49+9KMHxvPPP38c3lqClRz2YCWHy2FC24MJ7XKY0PbwjND6aqCNMHzUDBPaHp4RutadwlQqBY7jDlwb4zhhQtvDM0LXw8rqRccJE9oenhcaABMaTGg7uFpoRVHg8/mcPh7HYELbwzNCy3L9rZFZDc2EtoMrhK43fNTtMKHt4RmhG4k333wTCwsLWFhYwLVr10AIQXd3N3K5HHK5HK5evWrplr6deO211zAxMeF4u+bo6urCjRs3qObIZDLI5/NUcwwMDGBoaIhqjuHh4YOFNi82LkkS/H6/K0uOjY0NPHr0CI8ePYKiKCCE4Pr165ibm8Pc3ByKxaKx34pToQ+xdbpdc/T396NUKlHNceXKFUxPT1PNcf36dYyPj1PNcfv27YNraPMk2UAgAFmWWbfd/2ElhzU0TcMvf/lL/OpXv6I6e93SRaE+7lmSpDK53TwbnAltD5pCK4qC5557DqdOncIzzzwDQgi16zBLe6wEAgGoqopIJFJWZrAzNBPaCl//+ter1uj70pe+RCWXpYvCeDwOn89XtuWaoihVG/m4CSa0PWgKXavL9+Mf/ziVXE3Vy2GGCW2PozxDnzhxAl/5yleo5LIstKqqbPP6GjChD0ZRFJw+fRqnTp3CBz7wATz33HPHV0MDQDQaBSEE4XC4KtwKE9oeR9HL8dvf/ha///3vj7eXQ1Gc37z+KGBC28Mzdwplmc7m9bRhQtvDM0Krqurq3gwzT548we7uLnZ3d7G0tARCCFZWVrC5uYnNzU1sbW3h3XffdTQGBwfx97//3fF2zSHLMh4+fEg1x9jYGFZWVqjmmJmZQbFYpJqjVCodPDgpFoshEokYG3C69aKwUCjg9u3buH37Nvr6+kAIwR/+8Ae0t7ejvb0dXV1dGBkZcTT+9Kc/IZfLOd6uOURRRDabpZrj/PnzyGQyVHN0dnaiu7ubao6LFy9aWx+6XrgVVnLYwzMlR6PChLYHE9rlMKHt0fRCh8NhCIKw74wVtuA5E9oOxyq0qqoN1/dshgltj6YXutFhQtuDCe1yjkro3t5e7OzsUM0xNDSE9fV1qjlu3LiBlZUVqjmmpqYwPz9PNUexWGRCH4Zz585ha2uLao6uri6srq5SzdHf349CoUA1hyzLGB8fP9TzD+LAKViNChPaHo0gtD6u6Dvf+Q4ymUzN32FCHxImtHUOKzTw3nQuQghOnz6N733ve2VyN7TQ3/rWt+rGN7/5TZw6dQpf/epX91099bBx5swZfO1rX6Oa4zOf+Qy+/OUvU83x2c9+Fl/84hep5vjc5z6Hz3/+84du5wtf+AJOnDhhTBY4efIkPvShDyEWi+GVV15pXKF//vOf142f/OQnIITgpZde2nfTo8PG97//ffziF7+gmuNHP/oRXn75Zao5fvzjH+NnP/sZ1RzxeBwvvvjiodvRx+cTQnDy5EkQQvCJT3wCv/71rzE2Nta4Qu/HUZUct2/fxuPHj6nmmJ6exvb2NtUcpVKJek/K3bt3D106iaJoyPzJT34SqVSqbMLA2tpaYwqtqioURQGw9yKTyWTZVTAT2h6NILQ+MbtSYjMNKbQoikilUlAUBcL/b88LggBCCCRJAsCEtksjCG3l5lLDCa3LrGkaOI4re5E8zyMUCgE4OqF3dnbw3//+l2qOd999F//5z3+o5nj8+DH+/e9/U8/x5MkTqjmePHnSOEKrqmqMweZ53jgb6+gDqYCjE5rhPhpGaJ7njZWb9PrZjCzLxmpOTGjv0jBCE0L2nQIviiKi0SiA5hJakqSGWJN7P8zrutCmIYRWVfXA8dc8zxsf/Pb2Nn7zm98cwZHRRRAE+Hw+CP9fMLMR0Vew1fuiaU/dayih652p9LmPzYSiKEilUsYNhUalsneC4ziqi800hNDA3mqntdYI0TQNPM839ISE/Wh0oSuhvXBRwwgtSRIIIUgkElAUBaqqoq2tzejGa1aaSehUKlW2ii0NGkZoYK8e0+swQRCo/ulyC80itCiKR1IWNpTQXqQZhBZFsepGGC2Y0C6n0YUWRRHBYNDYaSufz7OLQi/TKHtD1kMvEc1Bcwc1JjSjqWBCM5oKJjSjqWBCM5oKJjSjqWBCM5oKJjSjqWBCM5oKJjSjqWBCU0CSpCMdAaiPPgTgqnHhmqbVnC5HEya0A1TeyuU47sg+SFVVy8YYu2lnBU3TEAgEjlRq97z6BkWSpGM9K/I8XzZ4yU1CA3tf9kgkcmT53PXqGwxJkhAMBuH3+xGJRIzB6/F4vGxlJ1EUEY/H4ff7EQqFIIoiZFlGJBKB3+9HS0tLWYmi7w8ZDAYRiUSqlmww/x4hpOy5+lS1SCSCYDCIlpaWqjOkIAgIhUIIBoOIxWJlzzcfe63H9NcjCAKCwaDxZdLb1N8Lcxs+n+/IztJM6EMiCELVGTocDhsj5ARBgN/vN6TUZ96Ew2Gj7o1Go2XTy8LhsPHl0EuKWiPuJEmq2umXEIJoNGq0HY/Hjdnw+s96bn36mvkMaj72eq8nFAqB53mjDX3wvv7FUBSl7EsSjUaRSqXqvodOwoQ+JFaErpTO5/OVnXXNZYuiKPD5fFU5ak1d0lfjNFM5mVhRlLIypNZyEOY614rQla9HFEWEQqG645yPckw3E/qQWBF6v/8H3pvqr/+71hZ6ter0WqLUqqH1x+otB2E+HitC15qsrC+50NLSUvX8Wu8BLZjQh4SG0PoafVZyV8q1n9B6zV3JQUL7fL6y17Pf2VYUxaq/QPW+BDRgQh8Sp4XWNM3yRVQqlapqez+hgb3ywtzNqKoqfD5fWT1vFrZyTRQr5UPl71T2xNCECX1IdCGSyaQhymGEBt47yyUSCSSTScRisZoXVZX1MXCw0PoagHrbwWCwTHBJkozXk0wmwXFc2UVpLaFTqRRisZjxHL/fX/b66l3U0oAJ7QD6WtX6n1nzVb55cXbz71d201X+jqqqRvfYfnceOY4rE7KWOJWPqaqKVCplrLNd7/Xoa55Uvp7Kiz+9p0N/jvn/zYtoHgVM6AanVtedmwiHw0fWZQcwoZsCURRdueiOpmlHKjPAhGY0GUxoRlPBhGY0FUxoRlPxP+2FRAHvFMiCAAAAAElFTkSuQmCC[/img][br]Write an equation giving the number of mcg of insulin, [math]m[/math], in the patient's body [math]h[/math] hours after receiving the injection.
After 3 hours, will the patient still have at least 10 mcg of insulin in their body? Explain how you know.