Question 4

(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.