Question

DIF eq help

Answer 1

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Answer 2

Suppose the difference between birth and death rates for a population of penguins is proportional to the population. At time t=0 there are 6 penguins and their number increased to 18 in 2 weeks.
a) write the diferential equation for P(t)
b) solve the resulting IVP for P(t)
c)When does the population reach 60 (rounded)
d)what eventually happens to the population?
e)when does this occur?

Answer 3

\[\frac{\mathrm d}{\mathrm dt} P(t) \propto P(t)\]...

Answer 4

p(14)=18
do i use pt()=p(0)*e^-kt?

Answer 5

where did you get the minus from?

Answer 6

set a proportionality constant ,

and solve the separable DE

Answer 7

3/14 would be the constant?

Answer 8

i can't check that without working

Answer 9

i think i just need a little direction on where to start

Answer 10

ools

Answer 11

sfgsdfg

Answer 12

fsdfgfsdfgdfsgdfsgdfgfdvbvbcxdfgdfsgsdf

Answer 13

a teacher is asking question to students - first time saw that

Answer 14

oh what are you doing?

Answer 15

hola me espanol

Answer 16

i am not a teacher right now. also, this isn't the type of math i would want to teach

Answer 17

are u spanish

Answer 18

i am not. but i can speak spanish. i took 6 years of it in university.

Answer 19

i am also just learning spanish at school for 1 month

Answer 20

hola me llamo mavi

Answer 21

como estas

Answer 22

u dint answer means u dont know spanish

Answer 23

\[\frac{dP}{dt} = kP\]
\[\int\limits \frac{dP}{P} = \int\limits k dt\]
\[\ln P = kt + C\]
\[P = e^{kt +C} = C e^{kt}\]
intial value --> p(0) = 6 so C = 6
p(2) = 18
\[18 = 6 e^{2k}\]
\[k = \frac{\ln 3}{2}\]
\[P(t) = 6 (3^{t/2})\]
solve for when p = 60
\[6(3^{t/2}) = 60\]
\[\ln 3^{t/2} = \ln 10\]
\[t = \frac{2 \ln 10}{\ln 3} = 4.19 \]
eventually population blows up to infinity