SOLUTION: Please help me understand the following equation: V=A(1-K^-t/T) for K. I understand / both sides by A then subtracting both sides by 1. What to do with the -K?

Click here to see ALL problems on Equations

Question 755955: Please help me understand the following equation:
V=A(1-K^-t/T) for K.
I understand / both sides by A then subtracting both sides by 1. What to do with the -K?
Found 2 solutions by Theo, knighty2002uk:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the interpretation of this problem is now:

V = A * (1 - K^(-t/T))

divide both sides of this equation by A to get:

V/A = 1 - K^(-t/T)

subtract 1 from both sides of the equation to get:

V/A - 1 = -K^(-t/T)

multiply both sides of the equation by -1 to get:

1 - V/A = K^(-t/T)

this becomes:

1 - V/A = 1 / K^(t/T)

multiply both sides of this equation by K^(t/T)) and divide both sides of this equation by (1 - V/A) to get:

K^(t/T)) = 1 / (1 - V/A)

raise both sides of the equation by the power of T to get:

(K^(t/T))^T = (1 / (1 - V/A))^T

simplify this to get:

K^(t) = (1 / (1 - V/A))^T

take the t root of both sides of the equation to get:

((K^(t))^(1/t) = ((1 / (1 - V/A))^T)^(1/t)

simplify to get:

K = ((1 / (1 - V/A))^T)^(1/t)

which can also be written as:

K = root(t,((1 / (1 - V/A))^T))

which looks like this:

K =

the answer has been confirmed to be correct.

Answer by knighty2002uk(39) (Show Source):
You can put this solution on YOUR website!
Having looked at this I'd do it slightly differently.
Still divide both sides by A to begin with to give

Rather than move the 1 lets make K (the subject a positive number as it's negative atm. Add K^(-t/T) to both side and subtract V/A from both sides to give

then using the rule of swapping powers, -t/T when moved to the other side of the equation reverses.