math question help please?

Question

Melanie told a secret to 3 friends. In one hour each friend told 3 people.In 2 hours those 3 told 3 more . How many people knew in 5 hours?

Answer 1

The answer is 40 people.

Melanie knows (1)
She told three friends (1+3=4)
After one hour, those 3 each told 3 others. (3x3=9, +4 = 13)
After two more hours, those 9 each told 3. (3x9=27, +13 = 40)

You can also graph this and count by hand if you want to double check the answer. If the question is worded correctly, the answer should be 40 people. If the question implies that each person continues to tell others over a 5 hour time period, then the answer will be much more. As far as time is concerned, it only takes 3 hours for 40 people to know the secret. The problem doesn't specify that each person continues to spread the secret, so the answer stands at 40 people.

Answer 2

Supposing that all people were told once (no two people told to the same person),

0 hour: 3
1 hour: 3*3
2 hours: 3*3*3

See a pattern?

5 hours: 3*3*3*3*3*3 = 3^6 = 729

In practice, some people will be told twice (tight circle of friends, etc), so the actual number, in real-life, will be smaller.

Answer 3

This is a geometric progression with r=3

4+9+27+81+243 +729=4 + ( 729*3-9)/2 =1093 people

Answer 4

1+3+9+27=40 people knew in 3 hrs. There is no info about 5 hrs.

Answer 5

this can be best worked out as an exponential function where y = a*b^x
where a is what you start with,
b is what happens to it and
x is how many times it happened....
FOR a: so you started with 3 ppl knowing
fFOR b: and what happened.... they told 3 ppl so what happened to it....it is times 3
FOR x: how many times... 5 times!
so a = 3
b=3
x=5
so it it 3*3^5=729 ppl were told...and if you add the fact that Melanie knew also, that makes 730 ppl.

Answer 6

3^5=243

Answer 7

N = ∑1 + 3 + 9 + 27 + ... + 3^(t + 1)
N = (3^7 - 1)/(3 - 1) = 1,093

Answer 8

3^(5+1)=3^6=729