Chapter 4.5, Problem 62E

Fruit Flies 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

$y=34.7{\left(1.0186\right)}^{-x}{x}^{-0.658}.$

b. Using your answer from part a, find the number of imagoes 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.