(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Denote by L(t) the length of a fish at time t, and assume that the fish grows according to:

dL/dt = k(34-L(t)) with L(0) = 2

a) solve the above equation

b)Use your solution in part a to determine k under the assumption that L(4) = 10.

c) Find the length of the fish when t = 10

d)Find the asymptotic length of the fish; that is, find lim[itex]_{t-->∞}[/itex]

2. Relevant equations

I attempted to solve part a by changing the equation to (dL/k(34-L(t))) = dt. I then took the integral of both sides raised the resulting equation to e. My answer was e^(1/-34k)*(ln(Lx) - ln(L(0)). This does not seem right to me but I tried to continue with the rest of the problem.

For part b, I attempted to solve for k and plug in 10 for L(x) and 2 for L(0). I ended up with k= e^-34*(10-2) = 1.37x10^-14. Once again I do not think this is correct.

As I mentioned previously, I do not believe I have done any of this problem correctly. I am only in my second quarter of calculus and am struggling. We were introduced to differential equations just the other day and I really do not get how to solve them. Any help would bee greatly appreciated as I have no idea how to proceed. Thank You.

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# Homework Help: Basic Differential Equations Problem (I Have No Idea What I Am Doing)

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