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. :)
100 km would be 100000 meters. Then you would need to know that if Usain bolt ran 100 meters every 9.54 sec then in 100000 meters he would have ran 9540 seconds which is also known has 159 minutes, which is more than 1 hour so your car is faster.
I can help you round 206834 and 194268 to its nearest thousands place. 207000 would be the estimate for the first number and 194000 would be the estimate for the second number.
