Mathematics, 03.04.2020 22:28 2023jpeterson
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
N(t)=⎧⎩⎨⎪⎪⎪⎪f(t)25t+150200+80t2+0 .05tfor0≤t<6for6≤t<8fort≥8
The number of fish in a pond at time t years is modeled by the function N defined above, where f is a continuous function such that f(0)=80.
(a) Find limt→∞N(t). Explain the meaning of limt→∞N(t) in the context of the problem.
(b) Is the function N continuous at t=8 ? Justify your answer.
(c) The function N is continuous at t=6 . Is there a time t , for 0≤t≤6 , at which N(t)=250 ? Justify your answer.
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