Cal in physical world rate of change (1 Viewer)

[BenBrownTown]

Hey just an easy simple question, so if i am to find k for a question and it is decreasing. Will my value of k be negative or is the negative supplied in the equation, so k is always a positive value?

Eg.
Ten kilograms of chlorine is placed in water and begins to dissolve. After t hours the amount A kg of undissolved chlorine is given by A=10e^-kt . What is the value of k given that A=3.6 and t=5 ?

would my answer for the value of k be 0.204 or -0.204 (3.d.p)
Cheers

 

[Carrotsticks]

In this case, since they already have the -k there for you, your k value should be positive.

 

[BenBrownTown]

In this case, since they already have the -k there for you, your k value should be positive.

Okay so if defined in a given formula it should be a positive constant value how about this one then

The population of a town is falling at a constant rate, so that after 25 years the population will have halved, and dP/dt =-kP , where P is the population of the town and t is the time in years. What is the value of k?

is it -0.028, or 0.028?

 

[Carrotsticks]

They already provided a minus there, so k will be positive.

Just think about what fits the scenario, rather than blindly substituting in positive or negative.

For example, if it is increasing, your rate MUST be positive. Whether your k value is positive or negative shouldn't be a problem. As long as it suits the question.

If it is decreasing, your rate MUST be negative likewise.

 

[BenBrownTown]

Yeah I get the fact that it doesn't matter about whether it is positive or negative, as you can just use common sense to figure out it is decreasing or increasing. But the question I am trying to solve is MC so they have provided a negative and positive solution for both, so that's why im trying to figure out what the value would be.

Would it be safe to say that a negative constant value of k is decreasing and a positive would be increasing or do I have to take into account the formula's and equations they have provided?

 

[D94]

Would it be safe to say that a negative constant value of k is decreasing and a positive would be increasing or do I have to take into account the formula's and equations they have provided?

No, don't think like that. Carrot has already said it twice that given the situation in the question, the value of k is positive. If you plug in a positive value of k, the the result is in the form dP/dt =-kP, but if you plug in a negative value of k, then the result is in the form dP/dt =-(-k)P = kP, which would be increasing. You want the final rate to be negative for a decreasing situation. If you were give dP/dt = -kP, how can it make sense to put in a negative value of k? It will change the rate to be positive, so that can't be decreasing.

You must take into account the equation given. The logic is in the situation.

 

[Denzel22]

You want the ultimate amount to be adverse for a reducing scenario. If you were give dP/dt = -kP, how can it sound right to put in a bad value of k? It will modify the amount to be good, so that can't be reducing.