linear function: The volume of water in a truck

[sparkleandpop]

The volume of water in a truck is determined by the length of time the sprayer is turned on. This relationship can be modeled by a linear function.

a. The slope of the function is -528 gallons/minute; describe the practical meaning of this value in the context of the problem.

b. (6, 832) is a coordinate point of the function. Explain the meaning of this point in the context of the problem.

c. Use the rate of change to determine the amount of water in the truck at 3.5 minutes.

d. Use the rate of change to determine the amount of time elapsed when there are 3000 gallons of water remaining in the tub.

e. Write the linear function f using meaningful variables that determines the amount of water remaining after t minutes of the sprayer running.

f. Determine the vertical intercept and explain its meaning in the context of the problem.

g. Determine the horizontal intercept and explain its meaning in the context of the problem.

h. Write the following statement using function notation and also as a coordinate point: After 4.1 minutes, the water truck sill contains 1835.2 gallons of water.

Please show work and formulas for each part of the questions. Thank you

 

[Deleted member 4993]

The volume of water in a truck is determined by the length of time the sprayer is turned on. This relationship can be modeled by a linear function.

a. The slope of the function is -528 gallons/minute; describe the practical meaning of this value in the context of the problem.

b. (6, 832) is a coordinate point of the function. Explain the meaning of this point in the context of the problem.

c. Use the rate of change to determine the amount of water in the truck at 3.5 minutes.

d. Use the rate of change to determine the amount of time elapsed when there are 3000 gallons of water remaining in the tub.

e. Write the linear function f using meaningful variables that determines the amount of water remaining after t minutes of the sprayer running.

f. Determine the vertical intercept and explain its meaning in the context of the problem.

g. Determine the horizontal intercept and explain its meaning in the context of the problem.

h. Write the following statement using function notation and also as a coordinate point: After 4.1 minutes, the water truck sill contains 1835.2 gallons of water.

Please show work and formulas for each part of the questions. Thank you

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[stapel]

The volume of water in a truck is determined by the length of time the sprayer is turned on. This relationship can be modeled by a linear function.

a. The slope of the function is -528 gallons/minute; describe the practical meaning of this value in the context of the problem.

To learn about slope and y-intercept in the context of word problems, try here. Then consider whether this slope indicates that water is running into, or draining out of, the truck's tub.

b. (6, 832) is a coordinate point of the function. Explain the meaning of this point in the context of the problem.

You are given that the volume is "determined by" (that is, dependent upon) the length of time. So which item, volume or time, is the independent value, and which is the value which is dependent upon that independent value?

In the point (6, 832), which number is the independent value? Which is the dependent value?

Given the context of the word problem and your definitions of the variables, what is the meaning of each of these numbers?

c. Use the rate of change to determine the amount of water in the truck at 3.5 minutes.

You are given the point (6, 832). You are given a rate of change relating the time and the volume. You are given here a time. Of 6 and 832, which is "time"? Use this information, and the given rate of change, to work backwards from the given point and the point wherein time is 6.

d. Use the rate of change to determine the amount of time elapsed when there are 3000 gallons of water remaining in the tub.

You are given the point (6, 832). You are given a rate of change relating the time and the volume. You are given here a volume. Of 6 and 832, which is "volume"? Use this information, and the given rate of change, to work backwards from the given point and the point wherein volume is 3,000.

e. Write the linear function f using meaningful variables that determines the amount of water remaining after t minutes of the sprayer running.

I'm not sure what they mean here by "using meaningful variables", since they've already specified that you're supposed to use "t" for "time" and "f(t)" for "volume" (rather than, say, V(t)). To be safe, I'd stick with the variables they've listed.

Plug the given point and the given slope into whichever of the formulas you prefer. (here)

f. Determine the vertical intercept and explain its meaning in the context of the problem.
g. Determine the horizontal intercept and explain its meaning in the context of the problem.

To learnm how to find intercepts, try here.

h. Write the following statement using function notation and also as a coordinate point: After 4.1 minutes, the water truck sill contains 1835.2 gallons of water.

You've found "y = f(t)" in part (e) above. Which of the numbers here represents time t? Which represents volume f(t)?

Please show work and formulas for each part of the questions.

As you saw in the "Read Before Posting" thread that you read before posting, showing work and formulas is kinda your job. So please reply with your answers to each of the sections above, at least as far as you're able to get. Thank you!