# Toronto Math Forum

## MAT244-2014F => MAT244 Math--Lectures => Topic started by: Hyunmin Jung on September 15, 2014, 03:08:15 AM

Title: 1.2 8 a)
Post 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

Title: Re: 1.2 8 a)
Post by: Victor Ivrii on September 15, 2014, 09:36:15 AM
I am rewriting using proper math input and slightly correcting
$dp/dt = rp$

a-b) 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*}