4. A new cafe opens in a country town. The manager of the cafe decides not to invest in advertising because the coffee is so good that he is confident that word will spread of the new cafe and its wonderful coffee. A marketing survey has shown that the percentage of the population in the country town who will hear of this new cafe is governed by the logistic model A P(!) = Btekt where P(t) represents the percentage of the town's population who hear about the cafe t days after the cafe opens. The constants A. B and & are to be determined from observations found by the market survey. The market survey of this word-of-mouth campaign finds that . On the day the cafe opened (at t = 0) 5% of the town's population had heard about the cafe. . After one week (t = 7) the word about the cafe has spread to 10% of the town's population. . Eventually, that is, after a very long time, everyone in the town will have heard about the cafe. (a) Given the three pieces of information provided by the marketing survey of this advertisement campaign, find the exact values of the constants A. B and k. Write the equation describing how many people will have heard about the cafe at time t days after the cafe opened. (b) Approximately what percentage of the town knew about the cafe 2 weeks after the cafe opened? (c) Approximately how many days after the cafe opened had half the population heard about the cafe? (d) Sketch the graph of P(t) = A Btekt' . Make sure you label the axes, any asymptotes and axes-intercepts