The use of iodine crystals is a popular way of making small quantities of water safe to drink. Crystals placed in a 1-ounce bottle of water will dissolve until the solution is saturated. After saturation, half of the solution is poured into a quart container of water, and after about an hour, the water is usually safe to drink. The half-empty 1-ounce bottle is then refilled, to be used again in the same way. Suppose that the concentration of iodine in the 1-ounce bottle t minutes after the crystals are introduced can be approximated by
C(t) = 250(1 - e-1) t ≥ 0
where C(t) is the concentration of iodine in micrograms per milliliter.
(A) What is the rate of change of the concentration after 1 minute? After 4 minutes?
(B) Graph C for 0 ≤ t≤ 5.