
f(6) = ?
Sorry if this is wrong section, I'm not sure where else to post. I am stuck with this problem:
f(x)= m * 2^{kx}
where
f(3)=27
f(4)=36
Question is: What is f(6)?
I can't figure how to solve either k or m; or how to substitute either of them for something useful. According to my textbook the answer is 64, but I have no idea how to get there. Any help is appreciated.

Re: f(6) = ?
You should end up with two equations:
$\displaystyle \displaystyle \begin{align*} 27 &= m\cdot 2^{3k} \\ 36 &= m \cdot 2^{4k} \end{align*}$
Do you see where these equations come from?
To eliminate one of the variables, the easiest thing to do would be to divide the second equation by the first...

Re: f(6) = ?
Keuko667
substitute x=4 first to the given relation and find : 36= m 2^(4k),
then substitute again x= 3 and find 27 = m 2^(3k)
divide these two equations and m disapears...you wil get 36/27=2^ k then get the logarithms of both sides to find the value of k .
the last step is to substitute k in one of the two equations and solve it for m ... After all these you know the complete formula of the function substitute x= 6 and find all what you need. As simple as such... try it....
MINOAS

Re: f(6) = ?
Sorry Prove it....when I saw it your answer was not there...
MINOAS

Re: f(6) = ?
I hadn't thought of dividing the pair, thank you very much for the help both!