Question

Let f(x) = 2^k + 9, where k is a real number. If f(3) : f(6) = 1:3, determine the value of f(9) - f(3).

Answer 1

Tougher problem...watch

Answer 2

I assume that f(x) = 2^x + 9, not k true?

Answer 3

Yeah i'm not sure how we're supposed to do much with this, it seems like k is a constant not a variable...

Answer 4

so the function f(x) is a constant function?

Answer 5

I've no idea, it seems like something is missing though

Answer 6

That really cant be, becuase if it is a constant function, then f(anything) = to that same constant.

It seems otherwise here.

Answer 7

Then you wouldnt have different ratios..for the same constant, everything will be in a 1:1 ratio

Answer 8

Yeah i think there's an x missing somewhere...

Answer 9

Oh sorry its 2^kx :)

Answer 10

is it \[2^{k} or k ^{2}\]

Answer 11

\[2^{kx} + 9\]

Answer 12

check where the function is inc or dec, from there you can get your answer...

Answer 13

Let f(x) = \[2^{kx} + 9\], where k is a real number. If f(3) : f(6) = 1:3, determine the value of f(9) - f(3).

Answer 14

@divu.mkr That's what was only stated here :(

Answer 15

first, you have to find the value of k. or at least related to k.
let's sub the conditions into the equation.\[f(3)=2^{3k}+9\]\[f(6)=2^{6k}+9\]
f(3):f(6)=1:3, which means \[3*(2^{3k}+9）=2^{6k}+9\]
notice that \[2^{6k}=(2^{3k})^{2}\]
now, if we set \[2^{3k}=y\], then we have another equation\[3*(y+9)=y^{2}+9\]
solve this for y, we will have the value of \[2^{3k}\]
then the rest is easy , just sub in the values, solve the problem.

Answer 16

didn't do the calculation, i'm gonna do it right now and let you know the answer.

Answer 17

wait, scratch what I said....

Answer 18

Yeah, that's what I was trying to do... lol....

Answer 19

for the equation \[3*(y+9)=y^{2}+9\], you will have y = 6 or -3. since k is a real number, so it's not possible to have \[2^{3k}=-3\]. so we have \[2^{3k}=6\]
now we are going to find the value of f(9)-f(3), which is
\[2^{9k}+9-(2^{3k}+9)\], which is simplified into \[(2^{3k})^{3}-2^{3k}\] we already know that 2^3k is 6. so the answer is 6^3-6=216-6=210

Answer 20

Cool problem. Well done, @linkinage .

Answer 21

@raechelvictoria getting this? if you have questions feel free to ask

Answer 22

@DebbieG thanks.

Answer 23

@linkinage Why can't it be (-3)^3 - 6?

Answer 24

like i explained, since k is a real number, it is not possible having 2^(3k) = -3

Answer 25

so 2^(3k) = 6 is rock solid and the only case we have to deal with.

Answer 26

@linkinage Oh okaaaaay. Thank you!

Answer 27

no worries.