MAT244-2014F > MAT244 Math--Lectures

1.2 8 a)

(1/1)

**Hyunmin Jung**:

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

**Victor Ivrii**:

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*}

Please fix your Name!

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