Toronto Math Forum
MAT2442014F => MAT244 MathLectures => Topic started by: Hyunmin Jung on September 15, 2014, 03:08:15 AM

Can someone verify that this is correct?
dp/dt = rp
a) Find the rate constant r if the population doubles in 30 days.
ln lpl = rt + C
lpl = e^(rt+ C)
p = e^rt*+e^C
Set + e^C = +c
p = c*e^rt
initial condition at t = 0
p0 = c*e^0
c = p0
population doubles in 30 days
let t be number of days
2p0 = p0(e^30r)
2 = e^30r
ln(2) = 30r
r = ln(2)/30

I am rewriting using proper math input and slightly correcting
$dp/dt = rp$
ab) Find the rate constant $r$ if the population doubles in 30 days.
\begin{gather*}
\ln p = rt + \ln C,\\
p = Ce^{rt},
\end{gather*}
The rest of your post is rather incomprehensible. To have it to multiply by $N$ in $T$ days we need to have $p(T)/p(0)= e^{rT}=N$ and then
\begin{equation*}
r=T^{1}\ln N
\end{equation*}
Please fix your Name!