The number of people who have heard a rumor, often grows exponentially, consider the room where that starts with three people, and where the number of people who have heard it doubles each day that it spreads which equation below, represents the above scenario

Answer 1

In the scenario where the number of people who have heard a rumor doubles each day, starting with 3 people, you can model this situation using an exponential growth equation.

Let \( P(t) \) represent the number of people who have heard the rumor after \( t \) days. Given that the number of people doubles each day, we can write the equation as:

\[ P(t) = P_0 \cdot 2^t \]

where \( P_0 \) is the initial number of people who have heard the rumor. Since we start with 3 people, we have:

\[ P_0 = 3 \]

Therefore, the equation that represents the scenario will be:

\[ P(t) = 3 \cdot 2^t \]

Here, \( t \) is the number of days since the rumor started spreading.

Answer 2

Could you put it in y= ?

Answer 3

Certainly! If we want to express the equation in the form \( y = \), we can set \( y \) as the number of people who have heard the rumor.

Based on the previous equation, where we established that the number of people doubles each day starting from 3, we can write:

\[ y = 3 \cdot 2^t \]

In this equation, \( y \) represents the number of people who have heard the rumor after \( t \) days.

Answer 4

And use x instead of t

Answer 5

Sure! If we use \( x \) instead of \( t \), the equation would be:

\[ y = 3 \cdot 2^x \]

In this equation, \( y \) represents the number of people who have heard the rumor after \( x \) days.

Answer 6

What does the dot between 3 and two mean

Answer 7

The dot between 3 and \( 2^x \) in the equation \( y = 3 \cdot 2^x \) signifies multiplication. So, the equation reads as:

\[ y = 3 \times 2^x \]

This means that to calculate \( y \), you take the initial number of people (which is 3) and multiply it by \( 2^x \), where \( x \) is the number of days. In simpler terms, as \( x \) increases, the value of \( y \) (the number of people who have heard the rumor) will grow exponentially due to the doubling effect each day.

Answer 8

How many people would know the rumor after 20 days raider answer with no spaces no commas

Answer 9

To find out how many people would know the rumor after 20 days, you can substitute \( x = 20 \) into the equation \( y = 3 \cdot 2^x \):

\[ y = 3 \cdot 2^{20} \]

Now, calculate \( 2^{20} \):

\[ 2^{20} = 1048576 \]

Now multiply this by 3:

\[ y = 3 \cdot 1048576 = 3145728 \]

Therefore, the total number of people who would know the rumor after 20 days is:

3145728