Janet told a secret to 4 friends. The next day, each of Janet's friends told the secret to 3 more people. The process continues for multiple days. Which function represents the number of people who will know the secret on the nthnth day?
A.
P(n)=3n+4P(n)=3n+4
B.
P(n)=4(3)nP(n)=4(3)n
C.
P(n)=4+(3)nP(n)=4+(3)n
D.
P(n)=n3+4P(n)=n3+4
look at the values for n
n #people
0 4
1 4*3
2 (4*3)*3 = 4*3^2
...
n 4*3^n
why do you repeat all the math? It's very distracting and annoying.
To solve this problem, we need to track the number of people who will know the secret on each day and look for a pattern. Let's break it down step by step:
On the first day, Janet told the secret to 4 friends. So, we have 4 people who know the secret on day 1.
On the second day, each of Janet's friends told the secret to 3 more people. Since there were 4 friends on day 1, we now have 4 friends * 3 people each = 12 people who know the secret on day 2.
On the third day, each of the 12 people from day 2 tells the secret to 3 more people. So, we have 12 people * 3 people each = 36 people who know the secret on day 3.
If we continue this process, we can see that the number of people who know the secret on each day can be represented by the formula P(n) = 4 * (3^n), where n is the number of days.
Therefore, the correct answer is B. P(n) = 4 * (3^n).