A study of the relation between the rate of reproduction in Drosophila (fruit flies) bred in bottles and the density of the mated population found that the number of imagoes(sexually mature adults) per mated female per day (y) can beapproximated bylog y = 1.54 - 0.008x - 0.658 log x,where x is the mean density of the mated population (measuredas flies per bottle) over a 16-day period. Source: Elements ofMathematical Biology.a. Show that the above equation is equivalent toy = 34.711.01862-xx-0.658.b. Using your answer from part a, find the number of imagesper mated female per day when the density isi. 20 flies per bottle;ii. 40 flies per bottle.c. Using your answer from part a, find the rate of change inthe number of imagoes per mated female per day with respect to the density when the density isi. 20 flies per bottle;ii. 40 flies per bottle
A study of the relation between the rate of reproduction in Drosophila (fruit flies) bred in bottles and the density of the mated population found that the number of imagoes
(sexually mature adults) per mated female per day (y) can be
approximated by
log y = 1.54 - 0.008x - 0.658 log x,
where x is the mean density of the mated population (measured
as flies per bottle) over a 16-day period. Source: Elements of
Mathematical Biology.
a. Show that the above equation is equivalent to
y = 34.711.01862-x
x-0.658.
b. Using your answer from part a, find the number of images
per mated female per day when the density is
i. 20 flies per bottle;
ii. 40 flies per bottle.
c. Using your answer from part a, find the rate of change in
the number of imagoes per mated female per day with respect to the density when the density is
i. 20 flies per bottle;
ii. 40 flies per bottle
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