I assume you have and understand the following skills. You will need them all. I hope you are for the long haul in this one because a long haul it is. Don't let that scare you off - 1st year University calculus will provide everything we will need.
1 - Solving 2 equations in 2 variables, m and k
This will give you the exact equation for dP/dt as a function of P
2 - How to find the maximum value of a function (in this case dP/dt) and for what
value of P it occurs
3 - How to use separation of variables to set up an integration
4 - How to use the technique of partial fractions to perform the integration
5 - How to find the constant of integration by using the initial condition.
6 - How to find the limit of P(t) as t ---> infinity
7 - How to solve an exponential equation using logarithms
Let's start with (1)
You are given to pieces of information that will allow you to find both m and k:
when P = 100 then dP/dt = 60 and when P = 200 then dP/dt = 90
That will give you 2 equations in m and k and you can solve them by elimination. You will then have the complete equation for dP/dt as a function of P. Let me know how you make out with that and then we can proceed to walk you through step 2.
You should be able to do c and d. They can be done by some simple plugging in and algebra.
Ian fowler what does downvote mean????
Downvote???? Really? What does that mean exactly? Can someone please explain. I have an answer of sorts but will withhold it for now.
You need the values for m and k. What did you get?
I assume you have and understand the following skills. You will need them all. I hope you are for the long haul in this one because a long haul it is. Don't let that scare you off - 1st year University calculus will provide everything we will need.
1 - Solving 2 equations in 2 variables, m and k
This will give you the exact equation for dP/dt as a function of P
2 - How to find the maximum value of a function (in this case dP/dt) and for what value of P it occurs
3 - How to use separation of variables to set up an integration
4 - How to use the technique of partial fractions to perform the integration
5 - How to find the constant of integration by using the initial condition.
6 - How to find the limit of P(t) as t ---> infinity
7 - How to solve an exponential equation using logarithms
Let's start with (1)
You are given to pieces of information that will allow you to find both m and k:
when P = 100 then dP/dt = 60 and when P = 200 then dP/dt = 90
That will give you 2 equations in m and k and you can solve them by elimination. You will then have the complete equation for dP/dt as a function of P. Let me know how you make out with that and then we can proceed to walk you through step 2.
Hope to hear from you soon.