Compare and Predict: models for highway mileage

[RicanGurl]

The amount of highway mileage (in thousands of miles) U(0) and R (t) in Urban areas and rural areas, respectiveley, can be modeled by the functions

U(t) = 12.88t + 625.48
R(t) = -13.38t + 3286.68

where t represents the number of years since 1980.

a. Compare U(0) with R(0). What do these values mean in terms of highway mileage?

b. Compare the slopes of U and R. What do these slopes mean in terms of highway mileage?

c. Predict when the highway mileage in urban areas will equal the highway mileage in rural areas.

d. Predict when the highway mileage in urban areas will be greater than the highway mileage in rural areas.

 

[Deleted member 4993]

Re: Compare and Predict (NEED HELP)

The amount of highway mileage (in thousands of miles) U(0) and R (t) in Urban areas and rural areas, respectiveley, can be modeled by the functions

Where is your Work?

                                    U(t) = 12.88t + 625.48
                                    R(t) = -13.38t + 3286.68
where t represents the number of years since 1980.

a. Compare U(0) with R(0). What do these values mean in terms of highway mileage?

Evaluate U(t) and R(t) at t = 0

b. Compare the slopes of U and R. What do these slopes mean in terms of highway mileage?

Slope of a straight line y = mx + b is m

What does slope mean for a straight line - it is a "rate" - rate of growth or decay.

c. Predict when the highway mileage in urban areas will equal the highway mileage in rural areas.

You tell me

d. Predict when the highway mileage in urban areas will be greater than the highway mileage in rural areas.

Still your turn

 

[RicanGurl]

my response

U(t) = 12.88t + 625.48
R(t) = -13.38t + 3286.68
where t represents the number of years since 1980.

a. Compare U(0) with R(0). What do these values mean in terms of highway mileage?

Evaluate U(t) and R(t) at t = 0

U(t) = 12.88(0) + 625.48
R(t) = -13.38(0) + 3286.68

U(t) = 625.48
R(t) =3286.68

You said to do that?

b. Compare the slopes of U and R. What do these slopes mean in terms of highway mileage?

c. Predict when the highway mileage in urban areas will equal the highway mileage in rural areas.

12.88t + 13.38t = 3286.68 - 625.48
26.26t = 2661.2

t ~ 101.34

what do you think?

d. Predict when the highway mileage in urban areas will be greater than the highway mileage in rural areas.

Confused on this one

 

[Deleted member 4993]

Re: my response

U(t) = 12.88t + 625.48
R(t) = -13.38t + 3286.68
where t represents the number of years since 1980.

a. Compare U(0) with R(0). What do these values mean in terms of highway mileage?

Evaluate U(t) and R(t) at t = 0

U(t) = 12.88(0) + 625.48
R(t) = -13.38(0) + 3286.68

U(0) = 625.48
R(0) =3286.68

- looks good - however, what does that result mean to you?

You said to do that?

Now answer the question:

What do these values mean in terms of highway mileage?

b. Compare the slopes of U and R. What do these slopes mean in terms of highway mileage?

c. Predict when the highway mileage in urban areas will equal the highway mileage in rural areas.

12.88t + 13.38t = 3286.68 - 625.48
26.26t = 2661.2

t ~ 101.34

what do you think? - looks good - however, what does that result mean to you?

d. Predict when the highway mileage in urban areas (U(t)) will be greater (>)than the highway mileage in rural areas(R(t)).

solve the inequality:

U(t) > R(t)

 

[RicanGurl]

U(t) = 12.88t + 625.48
R(t) = -13.38t + 3286.68
where t represents the number of years since 1980.

a. Compare U(0) with R(0). What do these values mean in terms of highway mileage?

Evaluate U(t) and R(t) at t = 0

U(t) = 12.88(0) + 625.48
R(t) = -13.38(0) + 3286.68

U(0) = 625.48
R(0) =3286.68

What do these values mean in terms of highway mileage?

That the amount of highway mileage of R is higher then U ... ?

b. Compare the slopes of U and R. What do these slopes mean in terms of highway mileage?

c. Predict when the highway mileage in urban areas will equal the highway mileage in rural areas.

12.88t + 13.38t = 3286.68 - 625.48
26.26t = 2661.2

t ~ 101.34

what do you think?

looks good - however, what does that result mean to you?

That the highway mileage in urban areas and in rural areas will be equal when at this point~ 101.34

Hm.......

d. Predict when the highway mileage in urban areas (U(t)) will be greater (>)than the highway mileage in rural areas(R(t)).

solve the inequality: U(t) > R(t)

Would that be meaning this 625.48 (t) < 3286.68 (t)

 

[stapel]

What do these values mean in terms of highway mileage?

That the amount of highway mileage of R is higher then U ... ?

Forever and always, the rural miles of road is greater than the urban miles? Is that how U(t) and R(t) are defined, as the amount of miles, fixed forever? :shock:

b. Compare the slopes of U and R. What do these slopes mean in terms of highway mileage?

What does slope usually mean the in context of word problems? How do you interpret these slopes, given how t, R, and U are defined?

That the highway mileage in urban areas and in rural areas will be equal when at this point~ 101.34

Is "101.34" the value of R, U, t, or something else? What does this value mean?

solve the inequality: U(t) > R(t)

Would that be meaning this 625.48 (t) < 3286.68 (t)

Is U(t) defined to be "625.48t"? Is R(t) defined to be "3286.68t"? If so, then solve that inequality. If not, then why are you using these functions?

You need to read the definitions and understand the steps. You're past the stage where you can blindly apply algorithms and expect the first number you run across to be the answer. I'm afraid you'll need to think to find the solutions here.

Eliz.

P.S. Your other thread on this question has been deleted. Please post questions only once, at least on any one tutoring site. Thank you.