Susanna heard some exciting news about a well-known celebrity.
Within a day she told 4 friends who hadn't heard the news yet.
By the next day each of those friends told 4 other people who also hadn't yet heard the news.
By the next day each of those people told four more, and so on.
- Assume the rumor continues to spread in this manner. Let \(N\) be the function that assigns to \(d\) the number of people who hear the rumor on the \(d^{\rm th}\) day. Write an expression for \(N(d)\).
- On which day will at least 100,000 people hear the rumor for the first time?
- How many people will hear the rumor for the first time on the 20th day?
- Is the answer to (c) realistic? Explain your reasoning.
Commentary
This problem is an exponential function example. The other tasks in this set illustrate F.BF.1a in the context of linear (Kimi and Jordan), quadratic (Skeleton Tower), and rational (Summer Intern) functions.