Posted by PPP on Wednesday, November 23, 2011 at 1:10pm.
A quantity has the value P at time t seconds and is decreasing at a rate proportional to sqrt(P).
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  Steve, Wednesday, November 23, 2011 at 5:01pm
we are told that
dP/dt = k * P^(1/2)
P^(1/2) dP = k dt
2P^(1/2) = kt + c
P = (2c  2kt)^2 = (abt)^2
if
a = 2c
b = 2k
Now, we are told that P(0) = 400
(a0)^2 = 400
a = 20 or 20
P(30) = 100
If a=20
(2030b)^2 = 100
so b = 1 or 1/3
If a = 20
(2030b)^2 = 100
so b = 1 or 1/3
So far, we have 4 combinations of values for a and b
I'll let you figure out P(50). Maybe you have more info that eliminates some of the choices.
Answer This Question
Related Questions
 calculus  A quantity has the value P at time t seconds and is decreasing at a ...
 Calculus  The rate of decay is proportional to the mass for radioactive ...
 Calculus  1) yy'e^x= 0, and y=4 when x=0 means that: A)y=xlnx^2+4 B)y^2=4x^2+...
 differential equation  in the theory of learning the rate at which the subject ...
 Calculus  Second Order Differential Equations  Posted by COFFEE on Monday, ...
 Calculus  Please look at my work below: Solve the initialvalue problem. y'' + ...
 calculus  Hydrocodone bitartrate is used as a cough suppressant. After the drug...
 Calculus (math)  Warfarin is a drug used as an anticoagulant. After ...
 calculus  A tissue culture grows until it has an area of 9 cm^2. A(t) is the ...
 Differential Equations  The velocity v of a freefalling skydiver is well ...
More Related Questions