Knowee
Questions
Features
Study Tools

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $505 to drive 460 mi and in June it cost her $565 to drive 700 mi.(a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model.C(d) = (b) Use part (a) to predict the cost of driving 1100 miles per month.$ (c) Draw the graph of the linear function. What does the slope represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the cost (in dollars) of driving.    It represents the cost (in dollars) per mile.It represents the distance (in miles) traveled.(d) What does the y-intercept represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the distance (in miles) traveled.    It represents the cost (in dollars) of driving.It represents the cost (in dollars) per mile.(e) Why does a linear function give a suitable model in this situation?A linear function is suitable because the monthly cost increases as the number of miles driven decreases.A linear function is suitable because the monthly cost increases even if the miles driven is constant.    A linear function is suitable because the monthly cost is fixed despite the fact that the miles driven may vary.A linear function is suitable because the monthly cost increases as the number of miles driven increases.

Question

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her 505todrive460miandinJuneitcosther505 to drive 460 mi and in June it cost her 565 to drive 700 mi.(a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model.C(d) = (b) Use part (a) to predict the cost of driving 1100 miles per month.$ (c) Draw the graph of the linear function. What does the slope represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the cost (in dollars) of driving.    It represents the cost (in dollars) per mile.It represents the distance (in miles) traveled.(d) What does the y-intercept represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the distance (in miles) traveled.    It represents the cost (in dollars) of driving.It represents the cost (in dollars) per mile.(e) Why does a linear function give a suitable model in this situation?A linear function is suitable because the monthly cost increases as the number of miles driven decreases.A linear function is suitable because the monthly cost increases even if the miles driven is constant.    A linear function is suitable because the monthly cost is fixed despite the fact that the miles driven may vary.A linear function is suitable because the monthly cost increases as the number of miles driven increases.

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

(a) To express the monthly cost C as a function of the distance driven d, we first need to find the rate of change (slope) of the cost with respect to the distance. We can do this by subtracting the costs and dividing by the difference in distance.

So, the slope (m) = (Cost in June - Cost in May) / (Distance in June - Distance in May) = (565565 - 505) / (700 miles - 460 miles) = 60/240miles=60 / 240 miles = 0.25 per mile

The cost function will then be C(d) = md + b, where m is the slope and b is the y-intercept. We can find b by substituting the cost and distance of one of the months into the equation. Let's use May:

505=505 = 0.25 * 460 miles + b => b = 505505 - 115 => b = $390

So, the cost function is C(d) = 0.25d+0.25d + 390

(b) To predict the cost of driving 1100 miles per month, we substitute d = 1100 into the cost function:

C(1100) = 0.251100+0.25 * 1100 + 390 = 275+275 + 390 = $665

(c) The graph of the linear function would be a straight line with a slope of 0.25andayinterceptof0.25 and a y-intercept of 390. The slope represents the cost (in dollars) per mile.

(d) The y-intercept represents the fixed cost (amount she pays even if she does not drive).

(e) A linear function is suitable because the monthly cost increases as the number of miles driven increases.

This problem has been solved

Similar Questions

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $505 to drive 460 mi and in June it cost her $565 to drive 700 mi.(a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model.C(d) = (b) Use part (a) to predict the cost of driving 1100 miles per month.$ (c) Draw the graph of the linear function.

The manager of a furniture factory finds that it costs $2400 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.(a) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear.C = 0.25d+390 Sketch the graph. (b) What is the slope of the graph?What does it represent?It represents the time (in days) to produce each additional chair.It represents the number of chairs produced.    It represents the cost (in dollars) of operating the factory daily.It represents the cost (in dollars) of producing each additional chair.(c) What is the y-intercept of the graph?What does it represent?It represents the time (in days) to produce each additional chair.It represents the number of chairs produced.    It represents the cost (in dollars) of producing each additional chair.It represents the fixed daily cost (in dollars) of operating the factory. Viewing Saved Work Revert to Last Response17.[–/6 Points]DETAILSSESSCALC2 1.2.014.MY NOTESASK YOUR TEACHERPRACTICE ANOTHERThe monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $505 to drive 460 mi and in June it cost her $565 to drive 700 mi.(a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model.C(d) = (b) Use part (a) to predict the cost of driving 1100 miles per month.$ (c) Draw the graph of the linear function. What does the slope represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the cost (in dollars) of driving.    It represents the cost (in dollars) per mile.It represents the distance (in miles) traveled.(d) What does the y-intercept represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the distance (in miles) traveled.    It represents the cost (in dollars) of driving.It represents the cost (in dollars) per mile.(e) Why does a linear function give a suitable model in this situation?A linear function is suitable because the monthly cost increases as the number of miles driven decreases.A linear function is suitable because the monthly cost increases even if the miles driven is constant.    A linear function is suitable because the monthly cost is fixed despite the fact that the miles driven may vary.A linear function is suitable because the monthly cost increases as the number of miles driven

Instructions: Interpret the slope of the given scenario.A cab company charges a $3$3 flat rate in addition to $1.50$1.50 per mile.In this context, the slope is equal to the change in Answer 1 Question 2 over the Answer 2 Question 2.The slope of this graph is $$ Answer 3 Question 2 per mile. (Enter your answer using proper money notation.)CheckQuestion 2

Suppose you are the owner of a dairy company that produces milk powder. There is a fixed cost 6.4 thousand dollars every month and variable cost 9.41 thousand dollars per ton of milk powder. Write down the monthly total cost function (dollars in thousands) in the quantity of production Q (in tonnes). What is the slope of this linear function? Question 2 Answer a. none of the others b. -0.68 c. 6.4 d. 8.10 e. 9.41

A freight train is carrying goods across the country. The number of gallons of fuel it has used varies directly with the distance it has traveled. See the graph below.y100200300400500600700800900x501001502002503003504000NumberofgallonsusedDistancetraveled(miles)(a) How many gallons does the train use per mile?gallon(s)(b) What is the slope of the graph?

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.