Find the n value of a function

[chwala]

1.
Given a curve y= x^n, where n is an integer. If the curve passes between the points (2,200) and (2,2000), determine the values of n

Homework Equations

The Attempt at a Solution

the n value by trial and error can be 2^8=256 2^9=512 and 2^10=1024. The correct answer to this problem is n=9. How did they arrive at the answer?[/B]

 

[SteamKing]

1.
Given a curve y= x^n, where n is an integer. If the curve passes between the points (2,200) and (2,2000), determine the values of n

Homework Equations

The Attempt at a Solution

the n value by trial and error can be 2^8=256 2^9=512 and 2^10=1024. The correct answer to this problem is n=9. How did they arrive at the answer?[/B]

The two points (2, 200) and (2, 2000) represent a vertical line. Have you copied these coordinates correctly?

 

[chwala]

The two points (2, 200) and (2, 2000) represent a vertical line. Have you copied these coordinates correctly?

Yes the question has been copied correctly from pure mathematics 1 hugh neill and Douglas quadling, Cambridge page 49, number 3

 

[chwala]

The two points (2, 200) and (2, 2000) represent a vertical line. Have you copied these coordinates correctly?

The two points don't represent a line.

 

[andrewkirk]

The correct answer to this problem is n=9.

Not necessarily. Say rather 'The author thought the correct answer was n=9'.

29 times out of 30 book answers are correct. The rest of the time they're not. Physicists are woefully underpaid and overworked and don't have time to check their drafts as meticulously as they'd like.

This may be the 30th case, or it may be one of the 29. What were the exact words of the question?

 

[chwala]

Note the ter

Not necessarily. Say rather 'The author thought the correct answer was n=9'.

29 times out of 30 book answers are correct. The rest of the time they're not. Physicists are woefully underpaid and overworked and don't have time to check their drafts as meticulously as they'd like.

This may be the 30th case, or it may be one of the 29. What were the exact words of the question?

note
The term between and not through ,I may refer you to check online on the problem.

 

[Ray Vickson]

1.
Given a curve y= x^n, where n is an integer. If the curve passes between the points (2,200) and (2,2000), determine the values of n

Homework Equations

The Attempt at a Solution

the n value by trial and error can be 2^8=256 2^9=512 and 2^10=1024. The correct answer to this problem is n=9. How did they arrive at the answer?[/B]

There is no curve in the world of the form $y = x^n$ that goes through the two points $(x,y) = (2,200)$ and $(x,y) = (2,2000)$ Both of these points have the same $x$-value, so how could they possibly have different values of $y$? The short answer is: they can't.

 

[chwala]

There is no curve in the world of the form $y = x^n$ that goes through the two points $(x,y) = (2,200)$ and $(x,y) = (2,2000)$ Both of these points have the same $x$-value, so how could they possibly have different values of $y$? The short answer is: they can't.

Sorry don't forget that it is 2 raised to a power n And Not 2 raised to 0. The x values are not 2 and 2 respectively, but the y values are 200 and 2000 respectively

 

[HallsofIvy]

Sorry don't forget that it is 2 raised to a power n And Not 2 raised to 0. The x values are not 2 and 2 respectively, but the y values are 200 and 2000 respectively

Frankly, it looks like you don't know what you are talking about. y= x^n, for any n, is a function. It cannot give two different values of for x= 2. And now you say "The x values are not 2 and 2 respectively". What?? You said the graph passes through (2, 200) and (2, 2000). Both those points have x= 2.

You say "the correct answer is 9". That obviously is NOT correcr, 2^9= 512, not 200 or 2000.

 

[chwala]

Frankly, it looks like you don't know what you are talking about. y= x^n, for any n, is a function. It cannot give two different values of for x= 2. And now you say "The x values are not 2 and 2 respectively". What?? You said the graph passes through (2, 200) and (2, 2000). Both those points have x= 2.

You say "the correct answer is 9". That obviously is NOT correcr, 2^9= 512, not 200 or 2000.

The curve passes between (2,200) and (2,2000) whereby this two points lie on the curve y=x raised to n obviously the first x values should be (2 raised to 7..., where Y=200) for first point and similarly same for second point

 

[chwala]

N

The curve passes between (2,200) and (2,2000) whereby this two points lie on the curve y=x raised to n obviously the first x values should be (2 raised to 7..., where Y=200) for first point and similarly same for second point

n is an integer value, sorry...

 

[chwala]

Am usin

N

n is an integer value, sorry...

Smart phone

 

[Ray Vickson]

Sorry don't forget that it is 2 raised to a power n And Not 2 raised to 0. The x values are not 2 and 2 respectively, but the y values are 200 and 2000 respectively

I did not forget anything! YOU were the one that wrote (2,200), not me; and in Mathematics, the notation (2,200) stands for a point in the xy-plane where x = 2 and y = 200. If you mean $2^{200}$ then you must write it correctly, as 2^200 or 2²⁰⁰.

Anyway, assuming you meant $2^{200}$ and $2^{2000}$, there is still not enough information to solve the problem. Is $2^{200}$ a value of $y$, and if it is, what is the corresponding value of $x$? Is $2^{200}$ a value of $x$, and if so, what is the corresponding value of $y$? Or, do you mean that the curve goes through the point $(2^{200},2^{2000})$? If that is what you meant, then that should be what you write; in plain text it can be typed as (2^200,2^2000).

 

[chwala]

Thanks to all of you, I agree that there's a problem with the question,it can't be solved, I copied it accurately from the textbook. Regards

 

[HallsofIvy]

The curve passes between (2,200) and (2,2000) whereby this two points lie on the curve y=x raised to n obviously the first x values should be (2 raised to 7..., where Y=200) for first point and similarly same for second point

What are you talking about? 2^7= 128 NOT 200 so you cannot mean that "y= x^7" which would be saying 200= 2^7 which is NOT TRUE! Again, if y= 2^x then 2 raised to the same value, not two different values. Perhaps you are stating the problem incorrectly.

 

[andrewkirk]

Frankly, it looks like you don't know what you are talking about.

I think you misread the question. He wrote 'the curve passes between the points (2,200) and (2,2000)' not 'the curve passes through the points (2,200) and (2,2000)'. In other words, if we denote the curve by f(x), he is saying that 200<f(2)<2000.

The question makes sense (although it should say 'determine the possible values of n', not just 'determine the values of n'), as does chwala's concern about the answer in the book. The possible values of n are 8, 9 and 10, but the book suggests (I suspect erroneously) that only 9 is possible.

Communication seems to be hampered by the fact that chwala's smartphone doesn't seem to interact reliably with the PF site.

 

[chwala]

I think you misread the question. He wrote 'the curve passes between the points (2,200) and (2,2000)' not 'the curve passes through the points (2,200) and (2,2000)'. In other words, if we denote the curve by f(x), he is saying that 200<f(2)<2000.

The question makes sense (although it should say 'determine the possible values of n', not just 'determine the values of n'), as does chwala's concern about the answer in the book. The possible values of n are 8, 9 and 10, but the book suggests (I suspect erroneously) that only 9 is possible.

Communication seems to be hampered by the fact that chwala's smartphone doesn't seem to interact reliably with the PF site.

i have managed tyo solve the problem as follows:

y=x^n
200=2^n
giving us log 200= n log 2,
n=7.6
implying that since n is an integer, and we are looking for an n value passing between (2,200) and (2,2000), then n cannot be equal to 8.
Again 2000= 2^n,
log 2000=n log 2,
n= 10.9
implying that the n value we are looking for cannot be equal to 10, thus n=9

 

[andrewkirk]

n=7.6
implying that since n is an integer, and we are looking for an n value passing between (2,200) and (2,2000), then n cannot be equal to 8

That doesn't follow. It is not $n$ that is required to pass between those two points, but the curve $f_8(x)=x^n$. The curve $f_8(x)=x^8$ does that, as does $f_9(x)=x^9$ and $f_{10}(x)=x^{10}$.

Again I ask: What were the exact words of the questionin the book?

 

[chwala]

That doesn't follow. It is not $n$ that is required to pass between those two points, but the curve $f_8(x)=x^n$. The curve $f_8(x)=x^8$ does that, as does $f_9(x)=x^9$ and $f_{10}(x)=x^{10}$.

Again I ask: What were the exact words of the questionin the book?

Those were the exact words. I have quoted the textbook and author and the page in my previous posts. Regards

 

[HallsofIvy]

This is what you wrote initially:

1.
Given a curve y= x^n, where n is an integer. If the curve passes between the points (2,200) and (2,2000), determine the values of n

Homework Equations

The Attempt at a Solution

the n value by trial and error can be 2^8=256 2^9=512 and 2^10=1024. The correct answer to this problem is n=9. How did they arrive at the answer?[/B]

Perhaps we have been misinterpreting this. I thought you were asking for a curve that passed through the points (2, 200) and (2, 20000). Apparently you just want an integer value of n such that 2^n is somewhere between 200 and 2000. Yes, the "values (plural) of n" that satisfy that are 8, 9, and 10. 2^7= 128 which is less than 200 and 2^11= 2048 which is larger than 2000. If that is what the question is asking, then the answers are 8, 9, and 10, not just "9".

 

[chwala]

This is what you wrote initially:
Perhaps we have been misinterpreting this. I thought you were asking for a curve that passed through the points (2, 200) and (2, 20000). Apparently you just want an integer value of n such that 2^n is somewhere between 200 and 2000. Yes, the "values (plural) of n" that satisfy that are 8, 9, and 10. 2^7= 128 which is less than 200 and 2^11= 2048 which is larger than 2000. If that is what the question is asking, then the answers are 8, 9, and 10, not just "9".

Thanks, remember b is an integer implying the 7 point something us regarded or rather rounded off to 8 or 7 by truncation, and 10.9 rounded of to 11 or 10 by truncation, leaving us with the untouched integer value n is 9

 

[chwala]

This is what you wrote initially:
Perhaps we have been misinterpreting this. I thought you were asking for a curve that passed through the points (2, 200) and (2, 20000). Apparently you just want an integer value of n such that 2^n is somewhere between 200 and 2000. Yes, the "values (plural) of n" that satisfy that are 8, 9, and 10. 2^7= 128 which is less than 200 and 2^11= 2048 which is larger than 2000. If that is what the question is asking, then the answers are 8, 9, and 10, not just "9".

Thanks, remember n is an integer implying that the 7 point something is regarded or rather rounded off to 8 or 7 by truncation, and 10.9 rounded of to 11 or 10 by truncation, leaving us with the untouched integer value n is 9

 

[Ray Vickson]

Thanks, remember n is an integer implying that the 7 point something is regarded or rather rounded off to 8 or 7 by truncation, and 10.9 rounded of to 11 or 10 by truncation, leaving us with the untouched integer value n is 9

What are you trying to say? The issue is whether $200 < 2^8 <2000$, $200 < 2^9 < 2000$ and $200 < 2^{10} < 2000$. Those are all true, so it works for $n = 8, 9, 10$. That is all there is to it, no more, no less!

 

[chwala]

Agreed, tha

What are you trying to say? The issue is whether $200 < 2^8 <2000$, $200 < 2^9 < 2000$ and $200 < 2^{10} < 2000$. Those are all true, so it works for $n = 8, 9, 10$. That is all there is to it, no more, no less!

Agreed. Thanks