2022 TGM P2 Q2

In January \(2020\), a new cereal product is introduced through an advertising campaign to a population of \(1\) million potential customers. The rate at which the population hears about the product is assumed to be proportional to the number of people who are not yet aware of the product. After a year, half of the population has heard of the product.

1. How many will have heard of it by the end of \(2\) years?[7]
2. The company intends to stop the advertising campaign when \(95\%\) of the population is aware of the product. Find the month and year during which the company will stop the campaign.[2]