A study suggests that the extinction rate r(t) of marine animal families during

Question

A study suggests that the extinction rate r(t) of marine animal families during the Phanerozoic Eon can be modeled by the function r(t) = 3130/(t + 262) for 0 t 544, where t is time elapsed (in millions of years) since the beginning of the eon 544 million years ago. Thus, t = 544 refers to the present time, t = 540 is 4 million years ago, and so on. Compute the average of Rn and Ln with N = 10 to estimate the total number of families that became extinct in the periods 80 t 280. (Round your answer to three decimal places.)

Explanation / Answer

N=10

t =(280-80)/10 =20

Rn=20[ 3130/(90 + 262)+  3130/(100 + 262)+  3130/(110 + 262)+  3130/(120 + 262)+  3130/(130 + 262)+  3130/(140 + 262)+  3130/(150 + 262)+  3130/(160 + 262)+  3130/(170 + 262)+  3130/(180 + 262)+  3130/(190 + 262)+  3130/(200 + 262)+  3130/(210 + 262)+  3130/(220 + 262)+  3130/(230 + 262)+  3130/(240 + 262)+  3130/(250 + 262)+  3130/(260 + 262)+  3130/(270 + 262)+  3130/(280 + 262)]

Rn=62600[ 1/(90 + 262)+ 1/(100 + 262)+  1/(110 + 262)+  1/(120 + 262)+  1/(130 + 262)+ 1/(140 + 262)+  1/(150 + 262)+ 1/(160 + 262)+ 1/(170 + 262)+ 1/(180 + 262)+ 1/(190 + 262)+ 1/(200 + 262)+ 1/(210 + 262)+ 1/(220 + 262)+ 1/(230 + 262)+ 1/(240 + 262)+ 1/(250 + 262)+ 1/(260 + 262)+ 1/(270 + 262)+ 1/(280 + 262)]

=2852.950559

Ln=62600[ 1/(80 + 262)+ 1/(90 + 262)+ 1/(100 + 262)+  1/(110 + 262)+  1/(120 + 262)+  1/(130 + 262)+ 1/(140 + 262)+  1/(150 + 262)+ 1/(160 + 262)+ 1/(170 + 262)+ 1/(180 + 262)+ 1/(190 + 262)+ 1/(200 + 262)+ 1/(210 + 262)+ 1/(220 + 262)+ 1/(230 + 262)+ 1/(240 + 262)+ 1/(250 + 262)+ 1/(260 + 262)+ 1/(270 + 262) ]

=2916.489739

average =[2852.950559+2916.489739]/2

average=2884.720

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