# 2 "constants" + 2 variable question

• Oct 6th 2010, 02:10 PM
cb220
2 "constants" + 2 variable question
Hi, I'm not sure how I can solve this question.

\$\displaystyle 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...
• Oct 6th 2010, 02:19 PM
pickslides
Quote:

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

\$\displaystyle 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
• Oct 6th 2010, 02:23 PM
Quote:

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

\$\displaystyle 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

\$\displaystyle y=ka^x\$

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

\$\displaystyle 2y=ya^3\$

which gives a value for \$\displaystyle a^3\$ to start.
• Oct 6th 2010, 02:35 PM
cb220
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!