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Nasty differnation variables things

  • Thread starter thomas49th
  • Start date
  • #1
655
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A population grows in such a way that the rate of change of the population P at time t in days is proportional to P.

a) Write down a dfferential equation relating P and t

b) Show, by solving this equation, that the general solution of this equation may be written as [tex]P = Ak^{t}[/tex], where A and k are positive constants.


a) is easy:

dP/dt = kP

b) I dont know where to start

Can someone walk me through B please :)
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
[tex]\frac{dP}{dt} = kP[/tex]

[tex]\Rightarrow \frac{1}{P}\frac{dP}{dt}=k[/tex]


integrate both sides w.r.t. t
 
  • #3
655
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Can you show me how. I dont know how to intergrate this equation

Thanks :)
 
  • #4
655
0
hang on this is one of those stupid natural log ones

i know if y = a ^ x then dy/dx = a^x ln a

but how does that help?
 
  • #5
655
0
this is seperation of variables?
 
  • #6
rock.freak667
Homework Helper
6,230
31
this is seperation of variables?
Yes

[tex]\int \frac{1}{P}dP= \int k dt[/tex]



are you able to do the left side?
 

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