A group of marine biologists estimates that if certain conservation measures are implemented, the population of an endangered species of whale will be where N(t) denotes the population at the end of year t.Find the average population of the whales over the next 4 years.
A)644
B)646
C)639
D)636

Question

A group of marine biologists estimates that if certain conservation measures are implemented, the population of an endangered species of whale will be  where N(t) denotes the population at the end of year t.Find the average population of the whales over the next 4 years.
A)644 
B)646 
C)639 
D)636

Quizplus · Accepted Answer

We need to find the average population of whales over the next 4 years. Let's first find the population at the beginning and end of 4 years:
N(0) = population now = 11eb12b0_a974_cca0_b394_5f2096e3a4dd_TB7866_11
N(4) = population after 4 years

The average population over 4 years can be calculated as:
(Area under the curve for 4 years) / 4 
= [(N(4) + N(0)) / 2] * 4 / 4
= (N(4) + N(0)) / 2

We are given N(4), so we just need to find N(0), the population now:
N(0) = 11eb12b0_a974_cca0_b394_5f2096e3a4dd_TB7866_11

Therefore,
Average population over the next 4 years = (N(4) + N(0)) / 2
= (11eb12b0_a974_cca0_b394_5f2096e3a4dd_TB7866_11 + 11eb12b0_a974_cca0_b394_5f2096e3a4dd_TB7866_11) / 2
= 11eb12b0_a974_cca0_b394_5f2096e3a4dd_TB7866_11
= 639

Hence, the answer is C.

A Group of Marine Biologists Estimates That If Certain Conservation