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.