SOLUTION: A rare species of insect was discovered in the Amazon Rain Forest. In order to protect the species, environmentalists declare the insect endangered and transplant the insect to a p

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Question 397720: A rare species of insect was discovered in the Amazon Rain Forest. In order to protect the species, environmentalists declare the insect endangered and transplant the insect to a protected area. The population of the insect (t) months after being translated is given by P: P(t)= 50(1+0.5t)/(2+0.01t)
A. How many insects were discovered? In other words, what was the population when t=0?
B. What will the population be after 5 years?
C. Determine the horizontal asymptote of P(t). What is the largest population the protected area can sustain? Explain why. (Hint: use the calculator to help you. Choose a good window.)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have P%28t%29+=+50%281%2B.5t%29%2F%282%2B.01t%29+=+%2850+%2B+25t%29%2F%282+%2B+.01t%29

A: Just replace t = 0 to obtain P%280%29+=+25.

B: Replace t with 60 (since 60 months equals 5 years)

P%2860%29+=+%2850+%2B+25%2860%29%29%2F%282+%2B+.01%2860%29%29+=+596.1538 (round to 596)

C: A horizontal asymptote occurs when lim%28x-%3Einfinity%2C+%2850+%2B+25t%29%2F%282+%2B+.01t%29%29 is a finite number. In this case, lim%28x-%3Einfinity%2C+%2850+%2B+25t%29%2F%282+%2B+.01t%29%29+=+25%2F.01+=+2500, so 2500 is the maximum attainable population.