Math Is Fun Forum

Objective -

understand the concept of exponential growth...

Alejandro is making ballots for an election.  He cuts a single piece of paper in in half making 1 into 2...
He stacks the sheets and cuts them again making 2 into 4 stacks and cuts again making 8 and so on.

2 x 2 x 2 x 2 x 2 = 32     2^5    OR  "2 TO THE 5TH POWER"

A. Cut a sheet of paper as Alejandro did, and count the ballots after each cut.
     Make a table to show the number of ballots after I cut, 2 cuts, 3 cuts, and so on.

1st cut = 2 ballots
    2nd cut = 4 ballots
    3rd cut = 8 ballots
   
   

B. Look for a pattern in the way the number of ballots changes with each cut.
     Use your observations to extend your table to show the number of ballots
     for up to 10 cuts.

1st cut = 2 ballots
    2nd cut = 4 ballots
    3rd cut = 8 ballots
4th cut = 16 ballots
    5th cut = 32 ballots
    6th cut = 64 ballots
7th cut = 128 ballots... and so on

C.  If Alejandro made 20 cuts, how many ballots would he have? How many
     ballots would he have if he made 30 cuts?
   
    20 cuts = 1048576 ballots
    30 cuts =  1073741824 ballots 

... so far so good

here's where I need help,  I have spoken with the teacher and gotten the answers... I'd just like to see if others get the same answers.  Please provide your answers for the next two questions.

D. A stack of 250 sheets of the paper Alejandro is
     using is 1 inch high. How high would a stack
     of ballots be after 20 cuts? After 30 cuts?

E. How many cuts would Alejandro need to make
    to have a stack of ballots 1 foot high?

If you recognize the curriculum please also gave your opinion.

Thanks Chuck