Question

3. After her trip back from San Diego, Miss Kito decided to sell her car and use the proceeds to help support the entomological community. She made a donation to help protect a rare species of mosquito that environmentalists declared endangered. Thanks to Miss Kito’s generosity, the insects were transplanted to a protected area. The population P (in thousands) of the insect in t months after being transplanted is: P() = 2.5+50 0.01+2 a. [4 pts] Evaluate P(0). Using a complete sentence and appropriate units explain what this answer means in the context of the problem. b. [4 pts] Approximately how many years will it take before the population reaches 77,000 mosquitos? Round your answer to the nearest whole number. Using a complete sentence and appropriate units explain what this answer means in the context of the problem

Answer 1

a. To evaluate P(0), we substitute 0 into the expression for P(t):

P(0) = 2.5 + 50 * 0.01 + 2

P(0) = 2.5 + 0.5 + 2

P(0) = 5

In the context of the problem, P(0) represents the population of the rare species of mosquito immediately after being transplanted to the protected area. The population is estimated to be 5,000 mosquitoes (since the expression is in thousands).

b. To determine approximately how many years it will take for the population to reach 77,000 mosquitoes, we need to find the value of t when P(t) equals 77.

P(t) = 2.5 + 50 * 0.01t + 2

77 = 2.5 + 50 * 0.01t + 2

77 = 4.5 + 0.5t

0.5t = 72.5

t ≈ 145

Rounding to the nearest whole number, it will take approximately 145 years for the population of mosquitoes to reach 77,000.

In the context of the problem, this means that it will take a considerable amount of time for the population to reach the desired number. It emphasizes the slow growth rate of the mosquito population and the importance of long-term conservation efforts.