Mathematics
OpenStudy (anonymous):

what is the change of rate for this pattern? In Out 1 1 2 0 3 -1 4 -2 5 ? 6 ? 7 ? a. 1 b. -1 c. -2 d. 2

terenzreignz (terenzreignz):

I hope you mean rate of change :/ this seems to imply that you have a constant rate of change... to do that, get two consecutive outputs and subtract them. Get their corresponding inputs, and subtract them. Divide the differences...

terenzreignz (terenzreignz):

Let's just take the first two, for simplicity... the first two outputs are 1 and 0. What's their difference?

OpenStudy (anonymous):

1

terenzreignz (terenzreignz):

Okay, now, I want you to be consistent with your order, okay, in this case, you subtracted the SECOND output, from the first. So when we deal with the INPUTS, I want you to also subtract the SECOND input from the first. Now then, the first two inputs, (corresponding to the first two outputs) are 1 and 2. What is their difference? (Again, consistency..)

OpenStudy (anonymous):

1

terenzreignz (terenzreignz):

What is the second input?

OpenStudy (anonymous):

2

OpenStudy (anonymous):

OH its -1!

terenzreignz (terenzreignz):

terenzreignz (terenzreignz):

Remember, rate of change = change in outputs, divided by change in inputs. But you MUST be consistent, or else you WILL get a wrong answer.

terenzreignz (terenzreignz):

Now, your final answer... Difference of the first two outputs = ? Difference of the first two inputs = ?

OpenStudy (anonymous):

outputs=-1 inputs=-1

terenzreignz (terenzreignz):

Show your work: How did you get -1 for outputs?

OpenStudy (anonymous):

0-1

terenzreignz (terenzreignz):

Okay, fine. Keep in mind that you subtracted the FIRST output from the second. Now how did you get the -1 for the inputs?

OpenStudy (anonymous):

1-2=-1

terenzreignz (terenzreignz):

1-2... You subtracted the SECOND input from the first... even after I told you time and again that you MUST be consistent. You can't subtract first from second with outputs, and then subtract second from first with inputs!!!!!! It has to be the SAME!

OpenStudy (anonymous):

im sorry, this is just confusing me! okay so would it be 2-1=1 for the inputs?

terenzreignz (terenzreignz):

yes... you know what, let's make it standard... when computing differences, unless specified, always subtract the one that came first.... okay? Just to be clear, what's the difference of the third and fourth inputs?

terenzreignz (terenzreignz):

Remember, subtract the one that came first... so, in this case, subtract the third (third comes before fourth) from the fourth input. So what do you get?

OpenStudy (anonymous):

4-3=1

terenzreignz (terenzreignz):

Good. In fact, you get the same difference as when you took the difference of the first and second inputs... as it should be. So... difference between first two outputs = -1 difference between first two inputs = 1 What's their quotient?

terenzreignz (terenzreignz):

$\Large \text{rate of change}= \frac{\text{difference in outputs}}{\text{difference in inputs}}$

OpenStudy (anonymous):

i got -1 divided by 1 = -1 is that my answer?

terenzreignz (terenzreignz):

Correct :)

OpenStudy (anonymous):

thank you so much

terenzreignz (terenzreignz):

You will get the same answer if you use the third and fourth inputs and outputs, by the way.

terenzreignz (terenzreignz):

or the second and third... etc. Even if they aren't consecutive, say, first and third... practice... you have to get -1 everytime.

OpenStudy (anonymous):

okay can you help me with another problem thats similar?

terenzreignz (terenzreignz):

Sure... but you lead the way ;)

OpenStudy (anonymous):

okay here it is term number numerical number 0 5 1 7 2 9 3 11 so 1-0=1 5-7=2

OpenStudy (anonymous):

2-1=1 9-7=2 and then 3-2=1 9-11=2 so would it be 2?

terenzreignz (terenzreignz):

How did you get 2? Did you divide? (And lol, way to go all the way o.O)

OpenStudy (anonymous):

no i just subtracted

terenzreignz (terenzreignz):

Well, figures... 2 is correct... IF you're asked for the rate of change...

OpenStudy (anonymous):

yes i am.

terenzreignz (terenzreignz):

By the way, shortcut.. if the inputs are all 1,2,3,4,5, etc

terenzreignz (terenzreignz):

IE, inputs are consecutive integers, then the rate of change is just the difference between two outputs.

terenzreignz (terenzreignz):

Remember to subtract the output that came BEFORE, okay?

OpenStudy (anonymous):

yes, that is what confused me. okay another question? for that first problem, would the expression be n-1?

terenzreignz (terenzreignz):

Nope...

terenzreignz (terenzreignz):

To test it, you have to replace the n with your input number, and you HAVE to get the output number. Try n = 1 1-1 = 0 But the first output is 1, not 0. So it can't be n-1

OpenStudy (anonymous):

okay so could it be -n+2?

terenzreignz (terenzreignz):

Try it. When you let n = 1, do you get the first output? When you let n = 2, do you get the second output? When you let n = 3, do you get the... well, you get the idea ;)

OpenStudy (anonymous):

oh no its n + 1!

terenzreignz (terenzreignz):

What I said above ^ Test it.

OpenStudy (anonymous):

no :( so n + 2?

terenzreignz (terenzreignz):

You'd be able to answer that for yourself if you just TEST it... Like how I tested your n-1. Let's test for the first (n = 1) When we input n = 1 We get... n - 1 1 - 1 0 But 0 is NOT the first output, therefore it can't be n-1 Remember, when you have your expression, when you input a value for n, you have to get the correct output.

OpenStudy (anonymous):

oh its -n+2 because -1+2=1!

terenzreignz (terenzreignz):

Well, I suppose... but be careful... don't be convinced because of one test... when you let n = 2, do you get the second output? Try to do at least 3 tests, just to be safe... if it passes 3, then chances are, that's the one.

OpenStudy (anonymous):

i did that, it is it and either way the other ones dont work. if you dont mind theres another question i keep doing and im not getting a answer. (its a rate of change problem)

terenzreignz (terenzreignz):

Okay, go.. but make it quick, I need to go soon :)

OpenStudy (anonymous):

okay i promise this is the last one. x y 2 5 4 11 6 17 8 23 10 29

OpenStudy (anonymous):

4-2=2 11-5=6

terenzreignz (terenzreignz):

OpenStudy (anonymous):

6-4=2 17-11=6 8-6=2 23-17=6 10-8=2 29-23=5

OpenStudy (anonymous):

i got 2 and 6

OpenStudy (anonymous):

it cant be both

terenzreignz (terenzreignz):

It isn't. Getting differences is only part of the solution, LOL The rate of change is the difference of outputs DIVIDED BY the difference in inputs XD

OpenStudy (anonymous):

OHH! 3!

terenzreignz (terenzreignz):

Yupperz

OpenStudy (anonymous):

thank you so much you have no idea how much you helped me! ill let you go now.

terenzreignz (terenzreignz):

That's why you get -1 in the first question, since 0-1 divided by 2-1 is -1/1 which is 1

terenzreignz (terenzreignz):

And THANK YOU lol It's good enough that you learned something today ^_^ Signing off now ------------- Terence out