Question

Did i do this correctly? (working out below) :)
Find the general solution of A_n=1.0105A_(n-1).

Answer 1

\[A_n = 1.0105A _{n-1}\]
The first step would be to move everything so it equals to 0 right?
\[A_n - 1.0105A_{n-1} = 0\]
And then i'm not too sure how to continue from here

Answer 2

Do we just assume that the solution is of the form \[x_n = Cm^n\]
So we sub it into the equation:
\[A_n - 1.0105A_{n-1} = 0\]
\[Cm^n - 1.0105Cm^{n-1} = 0\]
Then divide through by Cm^n-1 ??
So,
\[m-1.0105 = 0 \rightarrow m = 1.0105\]
then sub m into \[x_n = Cm^n\]
Therefore,
\[A_n = C(1.0105)^n\]
is the general solution?

Answer 3

yes it is , you are correct

Answer 4

excellent, thank you :)!