Suppose that the rabbit population on Mr. McGregor’s farm is given by p(t) =3550t/t+2, where p(t) =rabbit population and t = time in months since McGregor purchased the farm. a)Does the graph of the function have a vertical asymptote? If so, give the equation of the vertical asymptote and explain why this should concern or should not concern Mr. McGregor. If the function does not have a vertical asymptote, explain why. b)Determine the domain of the function in the context of this problem. c)Find the equation of the horizontal asymptote. What does it mean in this context? d)Does the function intercept its horizontal asymptote? If so, where? Show your work. e)Find all the t-intercepts and interpret their meaning in the context of this problem. Then find all the y-intercepts and interpret their meaning in the context of the problem. f)After how many months does the rabbit population reach 2500? Round to the nearest tenth.
Suppose that the rabbit population on Mr. McGregor’s farm is given by p(t) =3550t/t+2, where p(t) =rabbit population and t = time in months since McGregor purchased the farm.
a)Does the graph of the function have a vertical asymptote? If so, give the equation of the vertical asymptote and explain why this should concern or should not concern Mr. McGregor. If the function does not have a vertical asymptote, explain why.
b)Determine the domain of the function in the context of this problem.
c)Find the equation of the horizontal asymptote. What does it mean in this context?
d)Does the function intercept its horizontal asymptote? If so, where? Show your work.
e)Find all the t-intercepts and interpret their meaning in the context of this problem. Then find all the y-intercepts and interpret their meaning in the context of the problem.
f)After how many months does the rabbit population reach 2500? Round to the nearest tenth.
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