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.
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.
You need the values for m and k. What did you get?