Curve Equation

The question is from the gcse edexcel june 2008 calculator paper (q.25)

The sketch shows a curve with the equation y=ka^x where k and a are constants, and a > 0
The curve passes through the points (1,7) and (3, 175)
Calculate the value of k and the value of a....

Please help me!

Reply 1

Rocious

In the co-ordinate (1, 7) 1 is your x-coordinate and 7 is your y-coordinate

if y = ka^x

then 7 = ka^1

same for the other point.

Then you have two equations which you can solve.

Reply 2

hunty91

Substitute the values of x and y in and solve simultaneously.

Reply 3

Nandoz

So going by your methodology this should eventually turn into simultaneous equations like this:
7= ka^1
175=ka^3
what would you do next though :s

Reply 4

Rocious

Nandoz

So going by your methodology this should eventually turn into simultaneous equations like this:
7= ka^1
175=ka^3
what would you do next though :s

7 = ka \implies a = \frac{7}{k}

You can use this fact to write the second equation in terms of just k.

Reply 5

Nandoz

Rocious

7 = ka \implies a = \frac{7}{k}

You can use this fact to write the second equation in terms of just k.

ohh right...so you get 175= k (7/k)^3 but then how do you rearrange to get a value for k? sorry for not getting this

Reply 6

Nandoz

would you get 175= 343k^2?

Reply 7

Rocious

175 = k(\frac{7}{k})^3 \implies 175 = k(\frac{7^3}{k^3}) \implies 175 = \frac{343}{k^2}

Reply 8

Nandoz

Rocious

175 = k(\frac{7}{k})^3 \implies 175 = k(\frac{7^3}{k^3}) \implies 175 = \frac{343}{k^2}

oh so k= sqroot (343/175)?

Reply 9

Rocious

Nandoz

oh so k= sqroot (343/175)?

Well yeah.

BUT

there are 2 solutions to that equation.

However when you try to find a you realise that one of those isn't valid, so k = sqrt(343,175) is correct.

Reply 10

Nandoz

Thank you Rocious- rep added

Reply 11

Sophiemacyds

Couldn't you have done k/7 and then 245/7=35. If that's incorrect then is A simply 7/k?

Reply 12

TeeEm

Original post by Sophiemacyds

Couldn't you have done k/7 and then 245/7=35. If that's incorrect then is A simply 7/k?

putting the content aside, have you noticed the date when this question was debated?

Reply 13

Sophiemacyds

Original post by TeeEm

putting the content aside, have you noticed the date when this question was debated?

I just saw the date - I was looking for an answer as I needed help on this question on my summer maths homework. Was the content correct?

Reply 14

TeeEm

Original post by Sophiemacyds

I just saw the date - I was looking for an answer as I needed help on this question on my summer maths homework. Was the content correct?

I did not look at the conversation
My advice is to post a new thread with a photo/scan of the question and I am sure they will be some helpers soon

Reply 15

Sophiemacyds

Original post by TeeEm

I did not look at the conversation
My advice is to post a new thread with a photo/scan of the question and I am sure they will be some helpers soon

Okay - thanks! :smile:

Reply 16

MatthewBrennan

Wow 14 and 7 years after these people and now I'm doing this question!

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