Question

medal-----I just need help figuring out this question not just the answer please
The table below represents the velocity of a car as a function of time:


Time Velocity
(hour) (miles/hours)
x y
0 50
1 52
2 54
3 56


Part A: What is the y-intercept of the function, and what does this tell you about the car?

Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents.

Part C: What would be the domain of the function if the velocity of the car was measured until it reached 60

Answer 1

Help please

Answer 2

Could you please help me if you can @Nnesha or @whpalmer4 or if you know someone you can tag to help

Answer 3

What is the definition of the \(y\)-intercept?

Answer 4

yes here

Answer 5

So, what is the definition of the \(y\)-intercept?

Answer 6

it is the point on a graph when the x is equalled to 0....?

Answer 7

Well, it's the value of \(y\) at the point on the graph where \(x=0\). Also the point where the graph crosses the \(y\)-axis.

Answer 8

So if we graphed the data in the table, would the \(x\)-axis be time, or velocity?

Answer 9

x wold be time because the velocity would be y

Answer 10

good. so now you can tell me the answer to part A...

Answer 11

so when x is 0 y is 50

Answer 12

Yes. And as \(x\) represents time, that's the initial velocity of the car, right? 50 miles/hour

Answer 13

yes so all i have to write would be.... the y intercept would be 50 if x is 0 im not sure how to word it

Answer 14

How about "the y-intercept of the function is 50 miles/hour"?

Answer 15

ok ..... :) but it also says what does this tell you about the car? i dont know how to figure that out or does that answer the entire question ? @whpalmer4

Answer 16

If you look back a few responses, I think you will find that I made a comment about what that represents...

Answer 17

The data in the table shows the car starting at 50 mph and going faster with each passing hour, right?

Answer 18

yes by 2 miles per hour

Answer 19

no, but close: it changes by 2 miles per hour per hour...

Answer 20

or miles/hour^2

Answer 21

yes :) your right

Answer 22

no, "you're right" :-)

Answer 23

On to part B! How do you find the average rate of change?

Answer 24

average rate of change for an function f(x) is intervals from a to b so the formula is f(b)-f(a) over b-a

Answer 25

okay, do you understand how to translate your table values into a,b,f()?

Answer 26

@whpalmer4 i was reading my notes from class would F(a) be x and f (b) be y

Answer 27

so would it be from the table 52-50 over 1-0 ??? not sure

Answer 28

Well, \(x\) takes on the values of \(a\) and \(b\) and \(y = f(x)\)

So at \(x=1 \text{ hour}\) we have \(a = x = 1\text{ hour}\) and \(f(1) = \) what?

Answer 29

52

Answer 30

Yes. so \(a = 1\) and \(f(a) = 52\)

Now how about \(b\) and \(f(b)\)?

Answer 31

b =2 and f(b)=2

Answer 32

f(b) =54 oops

Answer 33

why does b = 2? and f(b) is the value of the function at x=b=2, which doesn't appear to be 2 when I read the table...

Here's the initial problem again:
Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents.
^^^^^^^^^

Answer 34

well, my attempt to underline "\(x=3\)" didn't work so well!

Answer 35

ohhh So b =3 and f(b)=56

Answer 36

yes! we are trying to find the average rate of change over that 2 hour span, so \(a\) is the value of \(x\) or \(t\) at the start, and \(b\) is the value of \(x\) or \(t\) at the end, and \(f(a)\) and \(f(b)\) are the values from the table.

Answer 37

So our average rate of change between \(a\) and \(b\) is as your formula states:

\[\text{avg rate of change} = \frac{f(b)-f(a)}{b-a}\]

Answer 38

Can you plug in the values?

Answer 39

56-52/ 3-1=4/2 =2

Answer 40

Okay, if you are going to write equations on one line like that, you MUST use parentheses appropriately to show what isn't being shown by position!

what you wrote is actually equal to this:
\[56 - \frac{52}{3} - 1 = \frac{4}{2}\]

I know that isn't what you meant.

(56-52)/(3-1) = 4/2 would unambiguously convey the intended meaning

Answer 41

What will the units for your answer be? miles? miles per hour? something else?

Answer 42

oh ok thanks for that tip and my units would be miles per hour or miles/hour

Answer 43

so ithe change of rate would be 2 miles per hour

Answer 44

right number, wrong unit

\[\frac{56 \text{ miles/hr} - 52 \text{ miles/hr}}{3\text{ hr} - 1\text{ hr}} = \frac{4\text{ miles/hr}}{2\text{ hr}} = 2 \text{miles/hr}^2\] \]

Answer 45

can you explain why is it hr^2

Answer 46

I dont know how to get the little 2 sorry

Answer 47

right? if we continue accelerating at this rate, for every hour that passes, we will increase our speed by 2 miles/hour. If we accelerate for 10 hours, we will add \[10\text{ hours}*2\frac{\text{ miles}}{\text{hour*hour}} = 10\cancel{\text{ hours}}*2\frac{\text{ miles}}{\text{hour}*\cancel{\text{hour}}} \]
\[= 20 \frac{\text{ miles}}{\text{hour}}\] to our speed

Answer 48

ohhh yes ........ :0

Answer 49

thanks for explaining it

Answer 50

my mom says we have to go to church can i see if your on later to finish :)

Answer 51

the way it "builds up" in physics terminology:

\[x = v t\]distance = speed * time
\[v = a t\]velocity = acceleration * time

Answer 52

Sure, say hi to the big guy for me :-)

Answer 53

lol i will thank you so much