amount donating doubles each day; find day 96 donate

[Frost Nova X]

Question: Student are donating food for a food drive. The amount of people that donate food doubles each day.3 people donate on day 1. on which day will 96 student donate food.

i know you need to make a chart...
Day people
1 3 But, the next question is make this chart into an equation. Our teacher said
2 6 3, x2, and x(which is 6) are in this equation and 96 is the answer. HELP
3 12
4 24
5 48
6 96

 

[Frost Nova X]

Re: PLEASE HELP FAST

Sorry, on the second line the words are all jumbled up but the 3 isnt part of the chart on the second line

 

[Deleted member 4993]

Re: PLEASE HELP FAST

Question:
Student are donating food for a food drive. The amount of people that donate food doubles each day.3 people donate on day 1. on which day will 96 student donate food.

i know you need to make a chart...

       Day            people
         1                  3  But, the next question is make this chart                                into  an equation. Our       teacher said 3, x2, and x(which is 6) are in this equation and 96 is the answer. HELP[/size]
         2                  6                                         
         3                  12
         4                  24
         5                  48
         6                  96

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
Hint:

Do you see a pattern in the second column?

 

[Frost Nova X]

Re: PLEASE HELP FAST

Sorry about nit specifying where im stuck i need help on the equation part, and in the second column i see 2 4 8 6...... im very confused -_-

 

[Deleted member 4993]

Re: PLEASE HELP FAST

[quote="Frost Nova X":hr405t2l]Question:
Student are donating food for a food drive. The amount of people that donate food doubles each day.3 people donate on day 1. on which day will 96 student donate food.

i know you need to make a chart...

       Day            people
         1              3 * 2^(1-1)
         2              3 * 2^(2-1)                                         
         3              3 * 2^(3-1)
         4              3 * 2^(4-1)
         5              3 * 2^(5-1)
         6              3 * 2^(6-1)

Hint:

Now what does it tell you?[/quote:hr405t2l]

 

[soroban]

Hello, Frost Nova X!

You certainly had the right idea.
The second part requires a bit of Imagination . . .

Student are donating food for a food drive.
The amount of people that donate food doubles each day.
Three people donate on day 1.
In which day will 96 students donate food?

i know you need to make a chart...

. . \(\displaystyle \begin{array}{|c|c|} \text{Day} & \text{People} \\ \hline 1&3 \\ 2&6 \\ 3&12 \\ 4&24 \\ 5&48 \\ 6&96 \\ \vdots & \vdots \\ \hline \end{array}\)


But, the next question is: Make this chart into an equation.

We must examine the sequence of numbers and hope to find a pattern.

Factoring the numbers, we find this rhythmic pattern:

. . \(\displaystyle \begin{array}{c|ccccc} \text{Day} & n \\ \hline 1 & 3 &=& 3\cdot1 &=& 3\cdot2^0 \\ 2 &6 &=& 3\cdot2 &=&3\cdot2^1 \\ 3 & 12 &=& 3\cdot4 &=& 3\cdot2^2 \\ 4 & 24 &=& 3\cdot8 &=& 3\cdot2^3 \\ 5 & 48 &=& 3\cdot16 &=&3\cdot2^4 \\ 6 & 96 &=&3\cdot32 &=&3\cdot2^5 \\ \vdots & \vdots && \vdots && \vdots \end{array}\)

\(\displaystyle \text{Every day, the number of people is: }\,\text{3 times a power-of-2.}\)

\(\displaystyle \text{We see that the power-of-2 is one less than the day-number.}\)

\(\displaystyle \text{Therefore, on the }n^{th}\text{ day, there will be: }\;P(n) \;=\;3\cdot2^{n-1}\text{ people.}\)

 

[Denis]

Soroban, may I ask why you're activating 3 months old posts?