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
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.
The correct algebraic expression that models the situation is: c) 3^w.
Here's why:
In the first week, one customer tells three friends, so there are 3^1 (3 to the power of 1) or 3 new customers who know about the product.
In the second week, each of those three new customers tells three friends, so there are 3^2 (3 squared) or 9 new customers who know about the product.
In the third week, each of those nine new customers tells three friends, so there are 3^3 (3 cubed) or 27 new customers who know about the product.
So the number of new customers who know about the product after w weeks can be represented by 3^w.