Thread: 2 "constants" + 2 variable question

1. 2 "constants" + 2 variable question

Hi, I'm not sure how I can solve this question.

$y = k(a^x)$

Given: whenever the value of x is increased by 3, the value of y is doubled. Also 'k' and 'a' are positive constants.

I need to determine the value of k and a. The question allows for them to be indeterminable.

I'd like to start by making some relation between x and y but I'm not sure if that's what I should do. Something like this:

2x = y + 3

But I don't know if doing that makes any sense, since they don't actually equal each other for most values of x and y...

From there I would've liked to move that equation around to isolate y and substitute that into the original equation. However that still leaves 3 variables. I've tried to re-arrange the equation to isolate a or k, but when I try to put in answer on the web-form it complains that 'k' is undefined for example. So it would seem I have to somehow find concrete numbers for a and k but I have no idea how...

2. Originally Posted by cb220
Hi, I'm not sure how I can solve this question.

$y = k(a^x)$

Given: whenever the value of x is increased by 3, the value of y is doubled. Also 'k' and 'a' are positive constants.

when x=0, then y=k

when x=3, then y= 2k

when x=6, then y= 2(2k) = 4k

when x=9, then y= 2(4k) = 8k

3. Originally Posted by cb220
Hi, I'm not sure how I can solve this question.

$y = k(a^x)$

Given: whenever the value of x is increased by 3, the value of y is doubled. Also 'k' and 'a' are positive constants.

I need to determine the value of k and a. The question allows for them to be indeterminable.

I'd like to start by making some relation between x and y but I'm not sure if that's what I should do. Something like this:

2x = y + 3

But I don't know if doing that makes any sense, since they don't actually equal each other for most values of x and y...

From there I would've liked to move that equation around to isolate y and substitute that into the original equation. However that still leaves 3 variables. I've tried to re-arrange the equation to isolate a or k, but when I try to put in answer on the web-form it complains that 'k' is undefined for example. So it would seem I have to somehow find concrete numbers for a and k but I have no idea how...
Maybe simplest is

$y=ka^x$

$2y=ka^{x+3}=ka^xa^3$

$2y=ya^3$

which gives a value for $a^3$ to start.

4. Thanks for the quick replies!

Hmm, wow I don't think I would've thought to do it like that if I looked at it for a hundred years heh. But it makes sense now that I see it. Thanks!