1.2+Requesting+a+Reward

7/ 12/08 AE Notes: Instead of writing out long products of the same factor, you can use exponential form. Example: You can write 2x2x2x2x2 as 2^5=32.

** 1.2 Requesting a Reward **


 * A) Make a table showing the number of rubas the king will place on squares 1 through 16 on the chessboard.**

A)
 * Square || Rubas ||
 * 1 || 1 ||
 * 2 || 2 ||
 * 3 || 4 ||
 * 4 || 8 ||
 * 5 || 16 ||
 * 6 || 32 ||
 * 7 || 64 ||
 * 8 || 128 ||
 * 9 || 256 ||
 * 10 || 512 ||
 * 11 || 1024 ||
 * 12 || 2048 ||
 * 13 || 4096 ||
 * 14 || 8192 ||
 * 15 || 16384 ||
 * 16 || 32768 ||


 * B)** **How does the number of rubas change from one square to the next?**

B) The number doubles each square.


 * C) How many rubas will be on square 20? On square 30? On square 64?**

C) On square 20 there will be 540288 rubas. On square 30 there will be 536870912 rubas. On square 64 there will be 18446744073709551616.


 * D)What is the first square which the king will first place at least 1000000 rubas?**

D) The first square that will have 1000000 rubas is square 21.


 * E)If a ruba had the value of a penny, what would be the dollar value of the rubas on square 10, 20, 30?**

E) For 10 it’d be 512. For 20 it would be 540288. For 30 it’d be 536870912.

**** 1) Graph the data for squares 1-10. **
 * Problem 1.2 Follow-Up

1) (At the top of the page!) 2) Write an equation for the relationship between the number if the square, n, and the number of ruubas, r.

** 2) My equation is Y=2n


 * 3) If a chessboard had 100 squares, how many rubas would be on square 100?**

3) There would be 1267650600228229401496703205376 rubas.


 * 4a) How are these 2 patterns of change similar?**

4a) They are similar because they both grew exponentially.


 * 4b) Write a relationship for problem 1.1.**

4b) My relationship is ^2n.