Solutions 10: Modeling with Linear Functions

Solutions to Try Its

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

2. 41,100; 2020

3. 21.15 miles

Solution to Odd-Numbered Exercises

1. Determine the independent variable. This is the variable upon which the output depends.

3. To determine the initial value, find the output when the input is equal to zero.

5. 6 square units

7. 20.012 square units

9. 2,300

11. 64,170

13. [latex]P\left(t\right)=75,000+2500t[/latex]

15. (–30, 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.

17. Ten years after the model began.

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

21. (–15, 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.

23. At age 5.8 months.

25. [latex]C\left(t\right)=12,025 - 205t[/latex]

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.

29. 2064

31. [latex]y=-2t+180[/latex]

33. In 2070, the company’s profit will be zero.

35. [latex]y=30t - 300[/latex]

37. (10, 0) In 1990, the profit earned zero profit.

39. Hawaii

41. During the year 1933

43. $105,620

45.

a. 696 people
b. 4 years
c. 174 people per year
d. 305 people
e. [latex]P\left(t\right)=305+174t[/latex]
f. 2219 people

47.

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

49.

a. [latex]P\left(t\right)=190t+4360[/latex]
b. 6640 moose

51.

a. [latex]R\left(t\right)=16 - 2.1t[/latex]
b. 5.5 billion cubic feet
c. During the year 2017

53. More than 133 minutes

55. More than $42,857.14 worth of jewelry

57. $66,666.67