1.1+Making+Ballots

toc 11/23/08 ESK

Big Idea
The rate at which many things grow or decay can often be described mathematically.

Essential Question
How can I describe a pattern of repeated multiplication?

Notes from Class
Exponential form

Standard form

Problem 1.1
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 1 cut, 2 cuts, 3 cuts and so on. B. Look for a patter in the way the number of ballots changes with each cut.Use your observastions to extend your table to show the number of ballots for up to 10 cuts. The number of ballots doubles. The numbers are the power of 2s. C.If Alejandro made 20 cuts, how many ballots would he have? How many ballots would he have if he made 30 cuts? He would have 1073741824 ballots in 20 cuts. In 30 cuts he would have 1073741824. D.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? After 20 cuts the stacks of paper would be __inch high. After 30 cuts the stacks of paper would be __inch high. E.How many cuts would Alejandro need to make to have a stack of ballots 1 foot high? To make 1 foot high they should make 3.5cuts.
 * Cuts || 1 || 2  || 3  || 4  || 5  || 6  || 7  || 8  || 9  || 10  ||
 * Numbers of Ballots || 2 || 4  || 8  || 16  || <span style="font-family: 바탕;">32  || <span style="font-family: 바탕;">64  || <span style="font-family: 바탕;">128  || <span style="font-family: 바탕;">256  || <span style="font-family: 바탕;">512  || <span style="font-family: 바탕;">1024  ||

Problem 1.1 Follow-Up
1. Write each expression in exponential form. a. 2^3 b. 5^4 c. 1.5^7 2.Write each expression in standard form. a. 128 b. 27 c. 74.088 3. Most calculators have a key for evaluating exponents. Find out how to use your calculator to evaluate exponents, and then write each of these expressions in standard form. a. 32768 b. 59049 c. 3325.25673 4. Explain how the expressions 5^2, 2^5, and 5x2 differ. 5^2 is 5x5, 2^5 is 2x2x2x2x2, and 5x2 is 10. All of them has different standard form. 5. You know that 5^2=25. How can you use this fact to evaluate 5^4? If I know the fact 5^2=25, we know that 5^4 is 625. Because 5x5x5x5 is same as 25x25. 6. The standard form for 5^10 is 9,765,625. How can you use this fact to evaluate 5^11? Since you know 5^10 is 9765625, then I would know that 5^11 is 48828125. Because if you mutiply 5 by 9765625 you would get 48828125.