Question 868004
{{{No=150}}}
{{{C=450}}} 
N=C/(1+((C-No)/No)*e^-r*t has mismatched brackets (3 opening parentheses, and 2 closing parentheses).
I thought that you must have meant N=C/(1+((C-No)/No)*e^-r*t),
showing that the entire 1+((C-No)/No)*e^-r*t expression is in the denominator.
{{{N=C/(1+((C-No)/No)*e^(-r*t))}}}<--->{{{C=N*(1+((C-No)/No)*e^(-r*t))}}}<--->{{{C/N=1+((C-No)/No)*e^(-r*t)}}}<--->{{{C/N-1=((C-No)/No)*e^(-r*t)}}}
{{{C/N-1=((C-No)/No)*e^(-r*t)}}}<--->{{{(C-N)/N=((C-No)/No)*e^(-r*t)}}}<--->{{{((C-N)/N)*(No/(C-No))=e^(-r*t)}}}
That looks good because if we think of {{{X=(C-N)/N}}} as The relative increase to to get to C from N,
{{{Xo=(C-No)/No=(450-150)/150=300/150=2}}}<-->{{{No/(C-No)=1/2}}} ,
and the equation {{{((C-N)/N)*(No/(C-No))=e^(-r*t)}}} can be re-written as
{{{X=Xo*e^(-r*t)}}}<-->{{{X/Xo=e^(-r*t)}}} , which makes sense as exponential decay.
Better yet, substituting {{{No/(C-No)=1/2}}} , we get
{{{((C-N)/N)*(1/2)=e^(-r*t)}}}<--->{{{(C-N)/"2 N"=e^(-r*t)}}}<--->{{{ln((C-N)/"2 N")=-r*t)}}}<--->{{{r=-(1/t)*ln((C-N)/"2 N")}}}<--->{{{r=(1/t)*ln(2N/(C-N))}}}