One week, you tell two of your friends a secret. The next week, each of them tell two people the secret, and the next week, each
of those people tell two more people. So the first week, two new people know the secret; the second week, four new people know the secret; the third week, eight new people know the secret, etc. How many people find out the secret on the sixth week? A. 32
B. 64
C. 128
D. 256
The trick here is to recognize that the number of <u>new</u> people who learn this information each week is in powers of 2.
Week 0: 2^0 = 1
Week 1: 2^1 = 2
Week 2: 2^2 = 4 (2*2)
Week 3: 2^3 = 8 (2*2*2)
So following this pattern, we can just plug in 6 for week 6 and see what our answer is:
Week 6: 2^6 = 64 (2*2*2*2*2*2)
* A quick note in calculating powers:
calculating 2*2 six times is a lot of work. You know what isn't? 2*2*2 (8). You know what also isn't? 8*8. That's right, 8*8 is also 64! So instead of calculating 2*2*2*2*2*2, you can just calculate 2^3*2^3, or 8*8. :)
the graph would start at (0,2) [2 points up from the origin] and then go over 3 up 2, and repeat that over 3 up 2 until you've completed your line to the extent needed
