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3. A local towing company charges $5.50 for each mile plus a reservation fee of $12. They tow a maximum of 30 miles. a. Write a formula for the function C(x), representing the total cost to tow the car.x miles. b. Determine C(8). Show your work. Write your answer as an ordered pair and interpret its meaning in a complete sentence. c. Determine x when C(x)= 100. Show your work. Write your answer as an ordered pair and interpret its meaning in a complete sentence. d. Practical domain (include units): ≤x≤. ≤C(x) ≤ e. Practical range (include units): f. Construct a good graph of C(x).

3. A local towing company charges $5.50 for each mile plus a reservation fee of $12. They tow a maximum of 30 miles. a. Write a formula for the function C(x), representing the total cost to tow the car.x miles. b. Determine C(8). Show your work. Write your answer as an ordered pair and interpret its meaning in a complete sentence. c. Determine x when C(x)= 100. Show your work. Write your answer as an ordered pair and interpret its meaning in a complete sentence. d. Practical domain (include units): ≤x≤. ≤C(x) ≤ e. Practical range (include units): f. Construct a good graph of C(x).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Unit 8: Formulas and Functions #### Review **3. A local towing company charges $5.50 for each mile plus a reservation fee of $12. They tow a maximum of 30 miles.** **a. Write a formula for the function C(x), representing the total cost to tow the car x miles.** *Answer:* \ C(x) = 5.50x + 12 **b. Determine C(8). Show your work. Write your answer as an ordered pair and interpret its meaning in a complete sentence.** *Calculation:* \ C(8) = 5.50(8) + 12 = 44 + 12 = 56 \ *(Ordered Pair:* (8, 56)) \ By towing a car 8 miles, the total cost will be $56. **c. Determine x when C(x) = 100. Show your work. Write your answer as an ordered pair and interpret its meaning in a complete sentence.** *Calculation:* \ 100 = 5.50x + 12 \ 100 - 12 = 5.50x \ 88 = 5.50x \ x = 88 / 5.50 \ x = 16 \ *(Ordered Pair:* (16, 100)) \ To achieve a total cost of $100, the car must be towed for 16 miles. **d. Practical domain (include units):** \ \(0\ \text{miles} \leq x \leq 30\ \text{miles}\) **e. Practical range (include units):** \ \( 12 \leq C(x) \leq 177 )\ **f. Construct a good graph of C(x).** *Graph Description:* \ There is an empty grid provided to construct the graph. The x-axis will represent the miles (x) ranging from 0 to 30, and the y-axis will represent the cost (C(x)) ranging from $12 to $177. The graph of C(x) = 5.50x + 12 will be a straight line starting from (0, 12) and ending at (30, 177). The slope of the line is 5.50, meaning the cost increases by $5.50 for each additional mile towed.
Transcribed Image Text:### Unit 8: Formulas and Functions #### Review **3. A local towing company charges $5.50 for each mile plus a reservation fee of $12. They tow a maximum of 30 miles.** **a. Write a formula for the function C(x), representing the total cost to tow the car x miles.** *Answer:* \ C(x) = 5.50x + 12 **b. Determine C(8). Show your work. Write your answer as an ordered pair and interpret its meaning in a complete sentence.** *Calculation:* \ C(8) = 5.50(8) + 12 = 44 + 12 = 56 \ *(Ordered Pair:* (8, 56)) \ By towing a car 8 miles, the total cost will be $56. **c. Determine x when C(x) = 100. Show your work. Write your answer as an ordered pair and interpret its meaning in a complete sentence.** *Calculation:* \ 100 = 5.50x + 12 \ 100 - 12 = 5.50x \ 88 = 5.50x \ x = 88 / 5.50 \ x = 16 \ *(Ordered Pair:* (16, 100)) \ To achieve a total cost of $100, the car must be towed for 16 miles. **d. Practical domain (include units):** \ \(0\ \text{miles} \leq x \leq 30\ \text{miles}\) **e. Practical range (include units):** \ \( 12 \leq C(x) \leq 177 )\ **f. Construct a good graph of C(x).** *Graph Description:* \ There is an empty grid provided to construct the graph. The x-axis will represent the miles (x) ranging from 0 to 30, and the y-axis will represent the cost (C(x)) ranging from $12 to $177. The graph of C(x) = 5.50x + 12 will be a straight line starting from (0, 12) and ending at (30, 177). The slope of the line is 5.50, meaning the cost increases by $5.50 for each additional mile towed.
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