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Math 103: College Algebra 3.3 applications HW Directions: Complete all problems on separate paper. For each problem, you must find a function to maximize or minimize. For full credit, the function must be correct. Upload pictures or a scan of your solutions no later than Monday, October 19, 11:59 p.m. CST. 1. You have a 1200-foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What are the dimensions of the largest such enclosure? 2. Your factory produces lemon-scented air fresheners. You know each unit is cheaper, the more your produce. But you also know that costs will eventually go up if you make too many, due to storage of the overstock. The guy in accounting says that your cost for producing x thousand units a day can be approximated by the formula C(x)=0.04x^2-8.504x+25302. Find the daily production level that will minimize your costs. 3. Find a pair of numbers whose product is a maximum if twice the first number plus the second number is 48. 4. The sum of the length and width of a rectangle is 25 cm. Find the maximum area. 5. A piece of wire 20 feet long is cut into two pieces and each piece is bent to form a square. Determine the length of the two pieces so that the sum of the areas of the two squares is a minimum. 6. You run a canoe-rental business on a small river. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. Use this information to attempt to maximize your income. What should you charge? 7. The table lists the number of Americans (in thousands) who are expected to be over 100 years old for selected years. Year 1994 1996 1998 2000 2002 2004 Number (in thousands) 50 56 65 75 94 110 a. Find a quadratic function to fit the data set. Write it in proper form. b. How many Americans will be over 100 years old in the year 2008? c. In what year will the number of Americans over 100 years old exceed 200,000? 8. There is a sweet "shoot a pumpkin out of a cannon" contest held in the middle of nowhere. To be fair, pumpkins of nearly equal size are launched each time. The table shows the horizontal distance (in feet) said pumpkins travel when launched at different angles. Angle (in degrees) 20 30 40 50 60 70 Distance (in feet) 372 462 509 501 437 323 a. Explain why it's practical to use a quadratic function to model this data set (and the reason can't just be because the scatter plot looks like a parabola-think about why this scatter plot should look like it does!). b. Find a quadratic function to fit the data set. Write it in proper form. c. Use your model to determine at which angle the pumpkin should be launched in order for it to travel the farthest.

          Math 103: College Algebra
3.3 applications HW
Directions: Complete all problems on separate paper. For each problem, you must find a function to maximize or minimize. For full credit, the function must be correct. Upload pictures or a scan of your solutions no later than Monday, October 19, 11:59 p.m. CST.
1. You have a 1200-foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What are the dimensions of the largest such enclosure?
2. Your factory produces lemon-scented air fresheners. You know each unit is cheaper, the more your produce. But you also know that costs will eventually go up if you make too many, due to storage of the overstock. The guy in accounting says that your cost for producing x thousand units a day can be approximated by the formula C(x)=0.04x^2-8.504x+25302. Find the daily production level that will minimize your costs.
3. Find a pair of numbers whose product is a maximum if twice the first number plus the second number is 48.
4. The sum of the length and width of a rectangle is 25 cm. Find the maximum area.
5. A piece of wire 20 feet long is cut into two pieces and each piece is bent to form a square. Determine the length of the two pieces so that the sum of the areas of the two squares is a minimum.
6. You run a canoe-rental business on a small river. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. Use this information to attempt to maximize your income. What should you charge?
7. The table lists the number of Americans (in thousands) who are expected to be over 100 years old for selected years.
Year 1994 1996 1998 2000 2002 2004
Number (in thousands) 50 56 65 75 94 110
a. Find a quadratic function to fit the data set. Write it in proper form.
b. How many Americans will be over 100 years old in the year 2008?
c. In what year will the number of Americans over 100 years old exceed 200,000?
8. There is a sweet "shoot a pumpkin out of a cannon" contest held in the middle of nowhere. To be fair, pumpkins of nearly equal size are launched each time. The table shows the horizontal distance (in feet) said pumpkins travel when launched at different angles.
Angle (in degrees) 20 30 40 50 60 70
Distance (in feet) 372 462 509 501 437 323
a. Explain why it's practical to use a quadratic function to model this data set (and the reason can't just be because the scatter plot looks like a parabola-think about why this scatter plot should look like it does!).
b. Find a quadratic function to fit the data set. Write it in proper form.
c. Use your model to determine at which angle the pumpkin should be launched in order for it to travel the farthest.

Math 103: College Algebra
3.3 applications HW
Directions: Complete all problems on separate paper. For each problem, you must find a function to maximize or minimize. For full credit, the function must be correct. Upload pictures or a scan of your solutions no later than Monday, October 19, 11:59 p.m. CST.
1. You have a 1200-foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What are the dimensions of the largest such enclosure?
2. Your factory produces lemon-scented air fresheners. You know each unit is cheaper, the more your produce. But you also know that costs will eventually go up if you make too many, due to storage of the overstock. The guy in accounting says that your cost for producing x thousand units a day can be approximated by the formula C(x)=0.04x^2-8.504x+25302. Find the daily production level that will minimize your costs.
3. Find a pair of numbers whose product is a maximum if twice the first number plus the second number is 48.
4. The sum of the length and width of a rectangle is 25 cm. Find the maximum area.
5. A piece of wire 20 feet long is cut into two pieces and each piece is bent to form a square. Determine the length of the two pieces so that the sum of the areas of the two squares is a minimum.
6. You run a canoe-rental business on a small river. You currently charge 12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. Use this information to attempt to maximize your income. What should you charge?
7. The table lists the number of Americans (in thousands) who are expected to be over 100 years old for selected years.
Year 1994 1996 1998 2000 2002 2004
Number (in thousands) 50 56 65 75 94 110
a. Find a quadratic function to fit the data set. Write it in proper form.
b. How many Americans will be over 100 years old in the year 2008?
c. In what year will the number of Americans over 100 years old exceed 200,000?
8. There is a sweet "shoot a pumpkin out of a cannon" contest held in the middle of nowhere. To be fair, pumpkins of nearly equal size are launched each time. The table shows the horizontal distance (in feet) said pumpkins travel when launched at different angles.
Angle (in degrees) 20 30 40 50 60 70
Distance (in feet) 372 462 509 501 437 323
a. Explain why it's practical to use a quadratic function to model this data set (and the reason can't just be because the scatter plot looks like a parabola-think about why this scatter plot should look like it does!).
b. Find a quadratic function to fit the data set. Write it in proper form.
c. Use your model to determine at which angle the pumpkin should be launched in order for it to travel the farthest.

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