Answer to Question #61005 in Calculus for Georgia

Question

(a) Let H(t) be the total weight of all the lobsters, in kg, after t months.
Find a formula for H(t), expressing it in simplest form, Since the number of lobsters in the tank in months is expresses as N(t)= 6000/(t^2+25) and the mean weight of lobsters in months is expressed as W(t)=1.5ln⁡(t/4+1)

(b) draw this function and find its first derivative, H'(t),


(c) Consider the graph of H'(t). By choosing a suitable option, determine the rate at which the total weight of all the lobsters is changing after 2 months and after 10 months. Explain the meaning of your answers with reference to their magnitude and sign.