Homework Soursep0 1 million at t0 M carrying capacity 100 million at t 400
p0= 1 million at t=0
M (carrying capacity)= 100 million at t= 400 hrs
equation given in problem is : P(T)= M*P0 / [P0 + (M - P0)e^-rt]
calculate the value for r
so far i have 1.0e^8 = 1.0e^14 / [(1.0e^6) + 9.9e^7e^-400r]
I am having difficulty using algebra to break up the denominator so i can solve for r. Any help will be greatly appreciated!
M (carrying capacity)= 100 million at t= 400 hrs
equation given in problem is : P(T)= M*P0 / [P0 + (M - P0)e^-rt]
calculate the value for r
so far i have 1.0e^8 = 1.0e^14 / [(1.0e^6) + 9.9e^7e^-400r]
I am having difficulty using algebra to break up the denominator so i can solve for r. Any help will be greatly appreciated!
Solution
P(T)= M*P0 / [P0 + (M - P0)e^-rt] [P0 + (M - P0)e^-rt] x P (T) = M*P0 1x10^6 +[(1x10^8 - 1x10^6)e^-400r] x 10^8 = 10^14 [(1x10^8 - 1x10^6)e^-400r]x100 = 1x10^6 -1 [(1x10^8 - 1x10^6)e^-400r]=1x10^6 -1 e^-400r= 1x10^6 -1/(1x10^8 - 1x10^6) e^-400r=0.010101 r =0.0114878 / hr![p0= 1 million at t=0 M (carrying capacity)= 100 million at t= 400 hrs equation given in problem is : P(T)= M*P0 / [P0 + (M - P0)e^-rt] calculate the value for r](/WebImages/26/p0-1-million-at-t0-m-carrying-capacity-100-million-at-t-400-1068174-1761559112-0.webp "p0= 1 million at t=0 M (carrying capacity)= 100 million at t= 400 hrs equation given in problem is : P(T)= M*P0 / [P0 + (M - P0)e^-rt] calculate the value for r")
