A company is trying out a new marketing technique. They begin by asking one customer to tell three friends about a product in the first week. The next week, each of those new customers tells three friends. So 3 new people know about the product the first week, 9 the second week, and 27 the third week. Let w represent the number of weeks. Which algebraic expression models the situation?

Question

A company is trying out a new marketing technique. They begin by asking one customer to tell three friends about a product in the first week. The next week, each of those new customers tells three friends. So 3 new people know about the product the first week, 9 the second week, and 27 the third week. Let w represent the number of weeks. Which algebraic expression models the situation?
a) 3w

b) w^3

c) 3^w

d) 3w^3

GPT 3.5 · Answer

The pattern suggests exponential growth, since the number of people knowing about the product triples each week.
To model this situation algebraically, we need to raise the base 3 to the power of the week number w.
Therefore, the correct algebraic expression is c) 3^w.