Exp. Growth/ Decay help!! (1 Viewer)

[NizDiz]

Can someone help with 17?, I seem to be half right on all. All help appreciated

 

[HeroicPandas]

"Show that eventually all chickens will be infected."

This means as:



^U MUST PROVE THIS USING LIMITS

This is because intially all chickens are healthy and P represents the numbers infected, so if P = 1000, it means all chickens are infected and if P = 0, no chickens are infected

(ii)At t = 0, one chicken is infected

so at t= 0, P = 1

sub into formula





Seconds part asks u: how man days (t=?) when P =500

Let P = 500



Solve, t = 0.0069... YEARS

MULTIPLY By 365 (i think...)

and u get t = 2.52 days = 2 days

(iii)



I skipped some steps in part (iii)

Sub in ce^(blah) simplify, common denominate etc and trust me, u will get it

 

[HeroicPandas]

lol and the Q13 question (located in ur PDF document) is a very funny textbook question

 

[NizDiz]

So for part (iii), do u just use quotient rule to differentiate and go from there?
All makes sense now, thanks heaps!!

 

[HeroicPandas]

So for part (iii), do u just use quotient rule to differentiate and go from there?
All makes sense now, thanks heaps!!

I didnt actually use quotient rule, but yeh u can use quotient rule

 

[NizDiz]

For part (iii), how do u go get dP/dt = P^2 (1000-P/P)? Everything above I get.

 

[HeroicPandas]

For part (iii), how do u go get dP/dt = P^2 (1000-P/P)? Everything above I get.

AT LEAST, did you try it urself? I gave u the ideas, all u just need to do is continue with the annoying algebra (not too complex)

 

[braintic]

Since you are given the answer, P(1000-P), you can just do it by substitution (after differentiating of course).

 

[NizDiz]

yeh got it now, thanks mate