Differentiating rational functions with unknown constants

[Idealistic]

Given N = A/(1 + Be[sup:seqfnlqc]-0.7t[/sup:seqfnlqc]) Find dN/dt

I got A(0.7Be[sup:seqfnlqc]-0.7t[/sup:seqfnlqc])/(1 + Be[sup:seqfnlqc]-0.7t[/sup:seqfnlqc])[sup:seqfnlqc]2[/sup:seqfnlqc]

Is this correct?

Also, Given dN/dt = 12, N = 20, and t = 0, find constants A and B.

20 = A/(1 + B), A = 20B + 20,

12 = A(0.7B)/(1 + B), 12 = (20 + 20B)(0.7B)/(1 + B), 12 = 20(1 + B)(0.7B)/(1 + B), 12 = 20(0.7B), B = 6/7

A = 20 + 20(6/7), A = 260/7 or 37 and 1/7

Are A and B Correct?

Also, What is the limit of N as t appraches infinity? I figured it is infinity because the end result is division by a very small number.

I am just wondering if my answers and methods are correct.

 

[royhaas]

Your limit will be \(\displaystyle A\), since the exponential will vanish. Your other calculations look OK.

 

[Idealistic]

Right, its A divided by (1 plus a very small number) ...so A.

Thanks