Question

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. 1. 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 ݀dth day. Write an expression for n(d).

Option 1: d
Option 2: 4d
Option 3: 4^d
Option 4: d^4

Answer 1

The expression for n(d), representing the number of people who hear the rumor on the dth day, is 4^d. Each day, the number of people who hear the news is multiplied by 4.

Step-by-step explanation:

The function n(d) represents the number of people who hear the rumor on the dth day. In this case, each person who hears the news tells 4 other people. So on the first day, the number of people who hear the news is 4 (assuming Susanna's 4 friends are the only ones who heard the news). On the second day, each of the 4 friends tells 4 new people, resulting in a total of 4 * 4 = 16 people hearing the news. On the third day, each of the 16 people tells 4 new people, resulting in a total of 16 * 4 = 64 people hearing the news. This pattern continues, with the number of people hearing the news being multiplied by 4 each day. Therefore, the expression for n(d) is 4^d.