Explanation Formula used: Period and Amplitude A sin B x and A cos B x : The graphs of f ( x ) = A sin B x and f ( x ) = A cos B x where A ≠ 0 and B ≠ 0 have period 2 π | B | and amplitude | A | . Calculation: It is given that the population of foxes in a certain region over a 2-year period is estimated to be P 1 ( t ) = 400 + 50 sin ( π t 12 ) where t represents the month and the population of rabbits in the same region at time t is given by P 2 ( t ) = 3000 + 500 cos ( π t 12 ) . From the equation P 1 ( t ) = 400 + 50 sin ( π t 12 ) , it is noticed that 50 sin ( π t 12 ) is in the form of A sin B x has period 2 π π 12 = 24 and its amplitude | A | = 50 . Now from the equation P 2 ( t ) = 3000 + 500 cos ( π t 12 ) , it is noticed that 500 cos ( π t 12 ) is in the form of A cos B x has period 2 π π 12 = 24 and its amplitude | A | = 500

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Chapter 12.2, Problem 50E

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To sketch: The graphs of two functions P1(t)=400+50sin(πt12) and P2(t)=3000+500cos(πt12) and then explain the relationship between the sizes of the two populations.

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Chapter 12.2, Problem 49E

Chapter 12.2, Problem 51E

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The graphs of two functions P 1 ( t ) = 400 + 50 sin ( π t 12 ) and P 2 ( t ) = 3000 + 500 cos ( π t 12 ) and then explain the relationship between the sizes of the two populations.

Solution Summary: The author illustrates the graphs of two functions P_1(t)=400+50mathrmsin

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To sketch: The graphs of two functions P1(t)=400+50sin(πt12) and P2(t)=3000+500cos(πt12) and then explain the relationship between the sizes of the two populations.

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