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August 30, 2014

August 30, 2014

Posted by **PPP** on Wednesday, November 23, 2011 at 2:47pm.

a) By forming and solving a suitable differential equation, show that P= (a - bt)^2 , where a and b are constants.

Given that when t= 0, P = 400,

b) find the value of a.

Given also that when t= 30, P = 100,

c) find the value of P when t = 50.

- calculus -
**bobpursley**, Wednesday, November 23, 2011 at 4:10pmdecreasing rate dP/dt= k sqrt (P)

dP/(sqrtP)= k dt

integrate both sides.

-1/2 sqrtP=kT+ C

square both sides

1/4 P= (C+kT)^2

P= 4 (C+kT)^2 and by choosing the constansts C, k

P= (a-bt)^2

400=(a-b*o)^2

a= 20

100=(20-b30)^2

10=20-30b

b=1/3

P=(20-1/3*50)^2=(20-17.7)^2=...

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