Question

Why does it make sense that the number of people who have heard a rumor would grow exponentially

Answer 1

Since people hear rumors they like to tell other people about it which means they would probably do the best thing. That’s how it grows exponentially.

Answer 2

Step-by-step:

I found your worksheet online of which explains more in detail the assignment. The rumor starts with 3 people and doubles each day that it spreads.

The formula for exponential growth is $ab^{x}$.

You can plug your formula into the equation to get $2\times 3^{x}$  

an alternative way to answer plug that formula into desmos graphing calculator and draw what shows up there under the question.

I will reply to my answer a psychological reason for this to happen too for my own entertainment.