Question 755955
the interpretation of this problem is now:


V = A * (1 - K<sup>(-t/T)</sup>)


divide both sides of this equation by A to get:


V/A = 1 - K<sup>(-t/T)</sup>


subtract 1 from both sides of the equation to get:


V/A - 1 = -K<sup>(-t/T)</sup>


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


1 - V/A = K<sup>(-t/T)</sup>


this becomes:


1 - V/A = 1 / K<sup>(t/T)</sup>


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


K<sup>(t/T)</sup>) = 1 / (1 - V/A)


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


(K<sup>(t/T)</sup>)<sup>T</sup> = (1 / (1 - V/A))<sup>T</sup>


simplify this to get:


K<sup>(t)</sup> = (1 / (1 - V/A))<sup>T</sup>


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


((K<sup>(t)</sup>)<sup>(1/t)</sup> = ((1 / (1 - V/A))<sup>T</sup>)<sup>(1/t)</sup>


simplify to get:


K = ((1 / (1 - V/A))<sup>T</sup>)<sup>(1/t)</sup>


which can also be written as:


K = root(t,((1 / (1 - V/A))<sup>T</sup>))


which looks like this:


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


the answer has been confirmed to be correct.