Case Study: Modeling with Elementary Functions: Quiz

Problem 1

Today you discover that a space ship has landed in your back yard, and tomorow you tell your next door neighbor. The day after that, you and your neighbor each tell one new person about the space ship. Each day thereafter, each person who knows tells a new person. What formula below gives the number of people who know about the space ship after x days?

  1. 1 + 2 + 4 + 8 + ... + 2x
  2. x2
  3. e2x
  4. 2x

Answers, problem 1

We can model the number of people who know about the space ship after x days as a power of two, ie 2x. This is because after the first day, you tell your next door neighbor and that makes 2 people who know. After the second day, the you and your neighbor both tell a new person, making 4 people who know about the space ship. After 3 days, the four people who know about the space ship each tell a new person, making 8 people who know about the space ship. We can see that the number of people who know about the space ship is increasing as a power of two. Therefore the answer is 2x

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