How do you solve this word problem?

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 P(t)=50(1+0.05t)/2+0.01t

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.

Answer 1

Hi, Sekarri

Here's how to solve this one. The population equation is: P(t) = 50(1+0.05t)/2 + 0.01t [P is in thousands]

Part A requires us to solve for t when P(t) = 40 thousand.

Therefore, we can write: 40 = 50(1 + 0.05t)/2 + 0.01t

Multiply through to simplify: 40 = (50 + 2.5t)/2 + 0.01t

40 = 25 + 1.25t + 0.01t

15 = 1.26t

t = 15/1.26 [dividing both sides by 1.26]

= 11.9 months or 12 months, rounding up

Part B: The limiting factors, as with any population, will be their environment, namely space, food and water.