Observe some examples or specific situations
Observe the common features
Make a general conclusion
Form a strong inductive conclusion of the sequence 0.5, 0.25, 0.125, 0.0625, ...
0.5 = 0.51 0.25 = (0.5)2 0.125 = (0.5)3 0.0625 = (0.5)4
Conclusion:(0.5)n ;n=1,2,3,4,...
Form a strong inductive conclusion of the sequence 1, 3, 5, 7, ...
1 = 2 (0) + 1 3 = 2 (1) + 1 5 = 2 (2) + 1 7 = 2 (3) + 1
Conclusion : 2n + 1 ; n = 0, 1, 2, ,3, ...
Understanding Planning a Conclusion Implementing the the problem strategy strategy
The diagram on the right (refer textbook) shows the growth of a cell which begins with cell A. On the first day, two new cells are produced. Every cell will produce two other cells on subsequent days. The number of cells growth is P(t) = 2t, where t is the number of days.
a) How many new cells will be produced on the 8th day?
b) On which day will the number of new cells become 2048?
UNDERSTANDING THE PROBLEM
i. Make a conclusion by deduction
ii. Calculate the number of new
cells on the 8th day
iii. t = 8
iv. Calculate P ( 8)
PLANNING A STRATEGY
Substitute t with 8 into P (t) = 2t
CONCLUSION
P( t ) = 256
256 new cells will be produces on the 8th day
IMPLEMENTING THE STRATEGY
P( 8 ) = 28 = 256
CHECK ANSWER
8TH DAY
2, 4, 8, 16, 32, 64, 128, 256
UNDERSTANDING THE PROBLEM
i. Calculate on which day the number of new cells is 2048.
ii. Calculate the value of t when P(t) = 2048
PLANNING A STRATEGY
Solve 2t = 2048
CONCLUSION
t = 11
The number of new cells is 2048 on the 11th day.
IMPLEMENTING THE STRATEGY
2t = 2048 211= 2048