Advertising A popular shoe manufacturer is planning to market a new style of tennis shoe in a city of 500,000 people. Using a prominent professional athlete as their spokesperson, the company's ad agency hopes to induce 35% of the people to buy the product. The ad agency estimates that these satisfied customers will convince 35% of 35% of 500,000 to buy a pair of shoes, and those will persuade 35% of 35% of 35% of 500,000, and so on.
a. Model this situation using sigma notation.
b. Find the total number of people that will buy the product as a result of the advertising campaign.
c. What percentage of the population is this?
d. What important assumption does the advertising agency make in proposing the figure found in part b to the shoe manufacturer?