The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number of bacteria present is given by ƒ(t) = 500e^0.1t, under certain storage conditions, where t is time in days after packing of the product and the value of ƒ(t) is in millions.
(a) If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take?
(b) If t = 0 corresponds to January 1, what date should be placed on the product?