SOLUTION: Hi, i was wondering whether you were able to help me rearrange the following formula to find r; No=150 C=450 N=C/(1+((C-No)/No)*e^-r*t Thankyou!!

Algebra ->  Exponents -> SOLUTION: Hi, i was wondering whether you were able to help me rearrange the following formula to find r; No=150 C=450 N=C/(1+((C-No)/No)*e^-r*t Thankyou!!      Log On


   

Question 868004: Hi,
i was wondering whether you were able to help me rearrange the following formula to find r;
No=150
C=450
N=C/(1+((C-No)/No)*e^-r*t
Thankyou!!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F%281%2B%28%28C-No%29%2FNo%29%2Ae%5E%28-r%2At%29%29<--->C=N%2A%281%2B%28%28C-No%29%2FNo%29%2Ae%5E%28-r%2At%29%29<--->C%2FN=1%2B%28%28C-No%29%2FNo%29%2Ae%5E%28-r%2At%29<--->C%2FN-1=%28%28C-No%29%2FNo%29%2Ae%5E%28-r%2At%29
C%2FN-1=%28%28C-No%29%2FNo%29%2Ae%5E%28-r%2At%29<--->%28C-N%29%2FN=%28%28C-No%29%2FNo%29%2Ae%5E%28-r%2At%29<--->%28%28C-N%29%2FN%29%2A%28No%2F%28C-No%29%29=e%5E%28-r%2At%29
That looks good because if we think of X=%28C-N%29%2FN as The relative increase to to get to C from N,
Xo=%28C-No%29%2FNo=%28450-150%29%2F150=300%2F150=2<-->No%2F%28C-No%29=1%2F2 ,
and the equation %28%28C-N%29%2FN%29%2A%28No%2F%28C-No%29%29=e%5E%28-r%2At%29 can be re-written as
X=Xo%2Ae%5E%28-r%2At%29<-->X%2FXo=e%5E%28-r%2At%29 , which makes sense as exponential decay.
Better yet, substituting No%2F%28C-No%29=1%2F2 , we get
%28%28C-N%29%2FN%29%2A%281%2F2%29=e%5E%28-r%2At%29<--->%28C-N%29%2F%222+N%22=e%5E%28-r%2At%29<--->ln%28%28C-N%29%2F%222+N%22%29=-r%2At%29<--->r=-%281%2Ft%29%2Aln%28%28C-N%29%2F%222+N%22%29<--->r=%281%2Ft%29%2Aln%282N%2F%28C-N%29%29