A research company started tracking the number of fish in a lake and noticed that the population was decreasing exponentially. After 3 months of tracking, there were 729 fish and after 6 months there were 27 fish. a)How many fish were in the lake when the research company started tracking?

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the correct answer is the section c

good luck on your studies! : )

david edward.

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hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb