(a) s'(t) =
80,000,000e-0.2t / (1+20,000e-0.2t)2.
Thus, s'(90) =
80,000,000e-0.2(90) / (1+20,000e-0.2(90))2
1.22, so that sales were dropping at a rate of 1.22 gift-packs per day.
(b) A similar calculation shows that s'(100)
0.16 gift-packs per day, showing that sales were declining more slowly.
Since s(100)
0.82, we can estimate that approximately 1 gift-pack was sold that day.