{"id":11004,"date":"2015-07-14T17:35:48","date_gmt":"2015-07-14T17:35:48","guid":{"rendered":"https:\/\/courses.candelalearning.com\/osprecalc\/?post_type=chapter&p=11004"},"modified":"2019-10-04T15:11:51","modified_gmt":"2019-10-04T15:11:51","slug":"solutions-10","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/solutions-10\/","title":{"raw":"Solutions 2.3: Modeling with Linear Functions","rendered":"Solutions 2.3: Modeling with Linear Functions"},"content":{"raw":"

Solutions to Try Its<\/h2>\r\n1.\u00a0[latex]C\\left(x\\right)=0.25x+25,000[\/latex] The y<\/em>-intercept is (0, 25,000). If the company does not produce a single doughnut, they still incur a cost of $25,000.\r\n\r\n2.\u00a041,100;\u00a02020\r\n\r\n3.\u00a021.15 miles\r\n

Solution to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0Determine the independent variable. This is the variable upon which the output depends.\r\n\r\n3. To determine the initial value, find the output when the input is equal to zero.\r\n\r\n5. 6 square units\r\n\r\n7.\u00a020.012 square units\r\n\r\n9.\u00a02,300\r\n\r\n11.\u00a064,170\r\n\r\n13.\u00a0[latex]P\\left(t\\right)=75,000+2500t[\/latex]\r\n\r\n15.\u00a0(\u201330, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.\r\n\r\n17.\u00a0Ten years after the model began.\r\n\r\n19.\u00a0[latex]W\\left(t\\right)=\\text{7}.\\text{5}t+0.\\text{5}[\/latex]\r\n\r\n21. (\u201315, 0): The x-intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. (0, 7.5): The baby weighed 7.5 pounds at birth.\r\n\r\n23.\u00a0At age 5.8 months.\r\n\r\n25.\u00a0[latex]C\\left(t\\right)=12,025 - 205t[\/latex]\r\n\r\n27. (58.7, 0): In roughly 59 years, the number of people inflicted with the common cold would be 0. (0, 12,025): Initially there were 12,025 people afflicted by the common cold.\r\n\r\n29.\u00a02064\r\n\r\n31.\u00a0[latex]y=-2t+180[\/latex]\r\n\r\n33.\u00a0In 2070, the company\u2019s profit will be zero.\r\n\r\n35.\u00a0[latex]y=30t - 300[\/latex]\r\n\r\n37.\u00a0(10, 0) In 1990, the profit earned zero profit.\r\n\r\n39.\u00a0Hawaii\r\n\r\n41.\u00a0During the year 1933\r\n\r\n43.\u00a0$105,620\r\n\r\n45.\r\n

a. 696 people\r\nb. 4 years\r\nc. 174 people per year\r\nd. 305 people\r\ne. [latex]P\\left(t\\right)=305+174t[\/latex]\r\nf. 2219 people<\/p>\r\n47.\r\n

a. [latex]C\\left(x\\right)=0.15x+10[\/latex]\r\nb. The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used\r\nc. $113.05<\/p>\r\n49.\r\n

a. [latex]P\\left(t\\right)=190t+4360[\/latex]\r\nb. 6640 moose<\/p>\r\n51.\r\n

a. [latex]R\\left(t\\right)=16 - 2.1t[\/latex]\r\nb. 5.5 billion cubic feet\r\nc. During the year 2017<\/p>\r\n53.\u00a0More than 133 minutes\r\n\r\n55.\u00a0More than $42,857.14 worth of jewelry\r\n\r\n57.\u00a0$66,666.67","rendered":"

Solutions to Try Its<\/h2>\n

1.\u00a0[latex]C\\left(x\\right)=0.25x+25,000[\/latex] The y<\/em>-intercept is (0, 25,000). If the company does not produce a single doughnut, they still incur a cost of $25,000.<\/p>\n

2.\u00a041,100;\u00a02020<\/p>\n

3.\u00a021.15 miles<\/p>\n

Solution to Odd-Numbered Exercises<\/h2>\n

1.\u00a0Determine the independent variable. This is the variable upon which the output depends.<\/p>\n

3. To determine the initial value, find the output when the input is equal to zero.<\/p>\n

5. 6 square units<\/p>\n

7.\u00a020.012 square units<\/p>\n

9.\u00a02,300<\/p>\n

11.\u00a064,170<\/p>\n

13.\u00a0[latex]P\\left(t\\right)=75,000+2500t[\/latex]<\/p>\n

15.\u00a0(\u201330, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.<\/p>\n

17.\u00a0Ten years after the model began.<\/p>\n

19.\u00a0[latex]W\\left(t\\right)=\\text{7}.\\text{5}t+0.\\text{5}[\/latex]<\/p>\n

21. (\u201315, 0): The x-intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. (0, 7.5): The baby weighed 7.5 pounds at birth.<\/p>\n

23.\u00a0At age 5.8 months.<\/p>\n

25.\u00a0[latex]C\\left(t\\right)=12,025 - 205t[\/latex]<\/p>\n

27. (58.7, 0): In roughly 59 years, the number of people inflicted with the common cold would be 0. (0, 12,025): Initially there were 12,025 people afflicted by the common cold.<\/p>\n

29.\u00a02064<\/p>\n

31.\u00a0[latex]y=-2t+180[\/latex]<\/p>\n

33.\u00a0In 2070, the company\u2019s profit will be zero.<\/p>\n

35.\u00a0[latex]y=30t - 300[\/latex]<\/p>\n

37.\u00a0(10, 0) In 1990, the profit earned zero profit.<\/p>\n

39.\u00a0Hawaii<\/p>\n

41.\u00a0During the year 1933<\/p>\n

43.\u00a0$105,620<\/p>\n

45.<\/p>\n

a. 696 people
\nb. 4 years
\nc. 174 people per year
\nd. 305 people
\ne. [latex]P\\left(t\\right)=305+174t[\/latex]
\nf. 2219 people<\/p>\n

47.<\/p>\n

a. [latex]C\\left(x\\right)=0.15x+10[\/latex]
\nb. The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used
\nc. $113.05<\/p>\n

49.<\/p>\n

a. [latex]P\\left(t\\right)=190t+4360[\/latex]
\nb. 6640 moose<\/p>\n

51.<\/p>\n

a. [latex]R\\left(t\\right)=16 - 2.1t[\/latex]
\nb. 5.5 billion cubic feet
\nc. During the year 2017<\/p>\n

53.\u00a0More than 133 minutes<\/p>\n

55.\u00a0More than $42,857.14 worth of jewelry<\/p>\n

57.\u00a0$66,666.67<\/p>\n\n\t\t\t

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