Solve this Calculus Problem

[Josh]

Let P(t) represent the number of wolves in a population at time t years, when t is greater than or equal to 0. The population P(t) is increasing at a rate directly proportional to 800 - P(t), where the constant of proportionality is k.

(a) If P(0) = 500, find P(t) in terms of t and k
(b) If P(2) = 700, find k
(c) Find lim P(t).
t --> infinity

 

[Tiamat]

why do you need this solved? homework?
this is a very simple elementary differential equations question. Have you tried it? What are your answers? If you still have trouble, i can look at it.

 

[Josh]

Originally posted by: Tiamat
why do you need this solved? homework?

im testing to see how smart people on this forum are

 

[newb111]

42

 

[TuxDave]

c) 800.

 

[Sqube]

Originally posted by: Josh

Originally posted by: Tiamat
why do you need this solved? homework?

im testing to see how smart people on this forum are

Remembering how to do calculus != smart

 

[sao123]

the answer is 41.9999nine99nine9....dotdotdot

 

[Josh]

Originally posted by: Tiamat
why do you need this solved? homework?
this is a very simple elementary differential equations question. Have you tried it? What are your answers? If you still have trouble, i can look at it.

I thought is was Exponential Growth & Decay. We got a couple of answers but those don't have anything to do w/ the 800-P(t). Thanks in advance for your help.

 

[nycxandy]

Originally posted by: Josh

Originally posted by: Tiamat
why do you need this solved? homework?
this is a very simple elementary differential equations question. Have you tried it? What are your answers? If you still have trouble, i can look at it.

I thought is was Exponential Growth & Decay. We got a couple of answers but those don't have anything to do w/ the 800-P(t). Thanks in advance for your help.

LOL? You're not asking for help. You're asking us to solve the answers for you. :thumbsdown:

 

[Josh]

Originally posted by: nycxandy

Originally posted by: Josh

Originally posted by: Tiamat
why do you need this solved? homework?
this is a very simple elementary differential equations question. Have you tried it? What are your answers? If you still have trouble, i can look at it.

I thought is was Exponential Growth & Decay. We got a couple of answers but those don't have anything to do w/ the 800-P(t). Thanks in advance for your help.

LOL? You're not asking for help. You're asking us to solve the answers for you. :thumbsdown:

I'm looking for an explanation because I am stuck.

 

[Fenixgoon]

dude this is such an easy problem. solve it yourself.

 

[JackBurton]

It's 0 or 1. The answer is always 0 or 1.

 

[Random Variable]

I get p(t)=800-300*exp[(-ln3/2)*t]

 

[Josh]

Originally posted by: Random Variable
I get p(t)=800-300*exp[(-ln3/2)*t]

How'd you get that..?

 

[JohnCU]

Originally posted by: Random Variable
I get p(t)=800-300*exp[(-ln3/2)*t]

e^ln(x) = x

 

[Random Variable]

Originally posted by: JohnCU

Originally posted by: Random Variable
I get p(t)=800-300*exp[(-ln3/2)*t]

e^ln(x) = x

sorry

p(t)= 800-300*3^(-t/2)

which doesn't really simplify matters

 

[BoomerD]

3

 

[Josh]

Originally posted by: Random Variable

Originally posted by: JohnCU

Originally posted by: Random Variable
I get p(t)=800-300*exp[(-ln3/2)*t]

e^ln(x) = x

sorry

p(t)= 800-300*3^(-t/2)

which doesn't really simplify matters

howd you arrive at this conclusion?

(this question is for my cousin - not for me & i am not familiar with calculus)

 

[Random Variable]

Originally posted by: Josh

Originally posted by: Random Variable

Originally posted by: JohnCU

Originally posted by: Random Variable
I get p(t)=800-300*exp[(-ln3/2)*t]

e^ln(x) = x

sorry

p(t)= 800-300*3^(-t/2)

which doesn't really simplify matters

howd you arrive at this conclusion?

(this question is for my cousin - not for me & i am not familiar with calculus)

dp/dt=k(800-p)
?dp/(800-p)=?kt
-ln(800-p)=kt + c
800-p=e^(-kt+c)
p=800-e^(-kt+c)=800-c*e^(-kt)

p(0)=500=800-c
c=300

p(2)=700=800-300*e^(-2k)
1/3=e^(-2k)
ln3=2k
k=ln3/2

p(t)=800-300*e^[-(ln3/2)t]=800-300*3^(-t/2)

 

[TuxDave]

Originally posted by: Random Variable

Originally posted by: Josh

Originally posted by: Random Variable

Originally posted by: JohnCU

Originally posted by: Random Variable
I get p(t)=800-300*exp[(-ln3/2)*t]

e^ln(x) = x

sorry

p(t)= 800-300*3^(-t/2)

which doesn't really simplify matters

howd you arrive at this conclusion?

(this question is for my cousin - not for me & i am not familiar with calculus)

dp/dt=k(800-p)
?dp/(800-p)=?kt
-ln(800-p)=kt + c
800-p=e^(-kt+c)
p=800-e^(-kt+c)=800-c*e^(-kt)

p(0)=500=800-c
c=300

p(2)=700=800-300*e^(-2k)
1/3=e^(-2k)
ln3=2k
k=ln3/2

p(t)=800-300*e^[-(ln3/2)t]=800-300*3^(-t/2)

winnar!