Thursday

January 29, 2015

January 29, 2015

Posted by **PPP** on Wednesday, November 23, 2011 at 1:10pm.

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 5:01pmwe 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

if

a = 2c

b = 2k

Now, we are told that P(0) = 400

(a-0)^2 = 400

a = 20 or -20

P(30) = 100

If a=20

(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**

**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. ...

Differential Equations - The velocity v of a freefalling skydiver is well ...