2.1 – Use Inductive Reasoning

Inductive Reasoning: Make predictions based on patterns Conjecture: An unproven statement that is based on observations Counterexample: A statement that contradicts a conjecture

1. Sketch the next figure in the pattern.

1. Sketch the next figure in the pattern.

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 5, 10, 15, 20 25, 30, 35 +5 +5 +5 +5

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 2, 6, 18, 54 162, 486, 1,458 x3 x3 x3 x3

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 3, -9, 27, -81 243, -729, 2,187 x-3 x-3 x-3 x-3

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 2, 3, 5, 8, 12 17, 23, 30 +1 +2 +3 +4 +5

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 2, 5, 11, 23 47, 95, 191 x2+1 x2+1 x2+1 x2+1

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 1, 1, 2, 3, 5, 8 13, 21, 34 1+1 1+2 2+3 3+5 5+8

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 3, 0, -3, -6, … -9, -12, -15 -3 -3 -3 -3

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 288, 144, 72, 36, … 18, 9, 2 2 2 2

3. Describe a pattern in the numbers 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. –1 +1

Any four-sided polygon is a square. 4. Show the conjecture is false by finding a counterexample. Any four-sided polygon is a square. Rectangle

4. Show the conjecture is false by finding a counterexample. The square root of a whole number x is always smaller than the number x 1

For any numbers x and y, where x  0, 4. Show the conjecture is false by finding a counterexample. For any numbers x and y, where x  0,

5. Use inductive reasoning to make a conclusion based on the following: The product of any two odd numbers is _________. Ex. 3  3 = 9 Ex. -1  5 = -5 Ex. 7  -9 = -63 odd

6. Suppose you are studying bacteria in biology class 6. Suppose you are studying bacteria in biology class. The table shows the number of bacteria after n doubling periods. Your teacher asks you to predict the number of bacteria after 7 doubling periods. What would your prediction be? 6 7 256 512 x2 x2 x2 x2 x2 x2 x2

7. John believes that his walking speed influences his heart rate 7. John believes that his walking speed influences his heart rate. He took several pulse measurements based on walking speed and found a line to match his data. a. What would you predict his heart rate would be if his walking speed was 2.5mph? 106

7. John believes that his walking speed influences his heart rate 7. John believes that his walking speed influences his heart rate. He took several pulse measurements based on walking speed and found a line to match his data. b. What speed is he walking if his pulse rate is 130? 4.0

HW Problem 2.1 75-76 1-17 odd, 22 # 17 Ans: Example: 25 = 10