Year 12s: what will be the first way you research your future options? >>

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Year 12s: what will be the first way you research your future options? >>

AS differentiation

Custardcream000

The function h is given by h(x) = k/x^n where k and n are positive integers. The points (1,100) and (2,25) lie on the graph.

I) determine values k and n

Original post by Custardcream000

The function h is given by h(x) = k/x^n where k and n are positive integers. The points (1,100) and (2,25) lie on the graph.

I) determine values k and n

Well, you know that

\displaystyle \frac{k}{1^n} = 100

and

\displaystyle \frac{k}{2^n} = 25

What can you do with this information?

Custardcream000

OP

Original post by Zacken

Well, you know that

\displaystyle \frac{k}{1^n} = 100

and

\displaystyle \frac{k}{2^n} = 25

What can you do with this information?

Ahh I get it do you sub in one of the values of what k=

Original post by Custardcream000

Ahh I get it do you sub in one of the values of what k=

You have two equations in two variables. Simultaneous equations.

Although this one is very easy, the first equation should give you k directly and substituting it into the second gives you an equation which you can solve for n.

Custardcream000

OP

Original post by Zacken

You have two equations in two variables. Simultaneous equations.

Although this one is very easy, the first equation should give you k directly and substituting it into the second gives you an equation which you can solve for n.

K= 100
And n = 2 but I don't know how I show that

Original post by Custardcream000

K= 100
And n = 2 but I don't know how I show that

If,

\frac{k}{1^n} = 100

and we know that 1^anything = 1 then what can you say about k?

Then, re-arrange the second equation:

\frac{k}{25} = 2^n

, take logs of both side or spot n by inspection.

Custardcream000

OP

Original post by Zacken

If,

\frac{k}{1^n} = 100

and we know that 1^anything = 1 then what can you say about k?

Then, re-arrange the second equation:

\frac{k}{25} = 2^n

, take logs of both side or spot n by inspection.

Thanks for your help, I understand it now

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