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 = (a-bt)^2
a = 2c
b = 2k
Now, we are told that P(0) = 400
(a-0)^2 = 400
a = 20 or -20
P(30) = 100
(20-30b)^2 = 100
so b = 1 or 1/3
If a = -20
(-20-30b)^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
More Related Questions
- calculus - A quantity has the value P at time t seconds and is decreasing at a ...
- Calculus - 1) yy'-e^x= 0, and y=4 when x=0 means that: A)y=x-lnx^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 - Hydrocodone bitartrate is used as a cough suppressant. After the drug...
- Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...
- 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 ...
- Calculus - A patient is given a drug intravenously at a rate of 43.2 mg/hour. ...
- calculus - Write and then solve for y = f(x) the differential equation for the ...