From your information, I can say:
and you can easily find from the initial population at t=0. But the initial derivative means . Now, taking this expression and substituting it into the first expression, can you not find a?
I have the DE, , which I've solved to give .
I'm also given that and that .
Q) Suppose that at time there are cells and that P(t) is increasing at the rate of cells per month. After 6 months the tumor has doubled (size and number of cells). Find a.
We can say that .
If the tumor has doubled in 6 months, then does this mean that
Also if is increasing at a rate of , I presume that , or is it ?
If someone could give me a gentle push in the right direction it would be much appreciated
Thanks a lot
Here's what I've come up with so far.
Using the fact that ,
Having trouble finding a second equation in terms of just and .
We also know that when , P(t) is increasing at cells per month.
Using the expression for , and using , we get the following:
Not sure what to do from here, how to eliminate the ?
Thanks again for anyone reading through this
Sorry I'm just carrying on with myself here aren't I, every time I post I seem to get a new idea how to tackle this problem.
From what I've said earlier, I've got the two following equations:
The second equation is true when , so what I thought is to use the value of when , ie .
This results in ,
Now if I put this value into my first equation, this gives me:
Using Maple I've solved this to give me a value of .
However I know that both and are positive and real constants, so obviously something has gone wrong??
Sorry about all these questions, you have the patience of a saint
I understand how you got from the two equations to give the answer for . I don't get how you formed these two equations though?
You have a , but didn't these cancel out in this equation, ?
Also I'm not sure where the has come from either? Obviously we need a constant of integration but didn't all this get dealt with when I first solved the differential equation in the first place to get an equation for ?
Sorry for the confusion, clearly something completely obvious I've failed too see
All I can say is thank you so much for the help, you've been an absolute life saver.