Question

A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species, environmentalists declared the insect endangered and transplanted the insect to a protected area. The population P (in thousands )of the insect in t months after being transplanted is ?(?) = 50(1+0.05?) 2+0.01?

a. Determine the number of months until the insect population reaches 40 thousand.

b. What is the limiting factor on the insect population as time progresses? Explain your answer.

c. Sketch a graph of the function using the window 0 ≤ x ≤ 700 and 0 ≤ y ≤ 300. Be sure to indicate the scale on the graph, at least 2 points and any asymptotes.

Answer 1