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Use inductive reasoning to predict the next number in the given sequence

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1. Use inductive reasoning to predict the next number in the given sequence.

   1, 4, 9, 16, 25, ?

2. An economist for a telecommunication company determines that the number of cell phones the company can sell at various prices can be represented in the following graph.

   

   • A bar graph has the labels "Cost (in dollars)" on the horizontal axis and "Cell phones sold" on the vertical axis.
   • At the value 200 on the horizontal axis, the height of the bar is 1,000,000.
   • At the value 300 on the horizontal axis, the height of the bar is 667,000.
   • At the value 400 on the horizontal axis, the height of the bar is 500,000.
   • At the value 500 on the horizontal axis, the height of the bar is 400,000.
   • At the value 600 on the horizontal axis, the height of the bar is 333,000.

   By inductive reasoning, will the company sell fewer or more cell phones if the price of the phone is $700?

3. The following graph shows the distance an athlete has run over 60 seconds.

   

   There is a line on a coordinate plane.
   • The horizontal axis is labeled "Time (seconds)" and the vertical axis is labeled "Distance (feet)."
   • Vertical gridlines go through 10, 20, 30, 40, 50, and 60 on the horizontal axis.
   • Horizontal gridlines go through 200, 400, 600, 800, 1000, and 1200 on the vertical axis.
   • The line begins at the point (0, 0) and moves up and to the right. It crosses through the points (10, 200), (20, 400), (30, 600), (40, 800), and (50, 1000) before it ends at (60, 1200).

   Use inductive reasoning to predict the distance (in feet) the athlete will run in 70 seconds.

4. A block on a table is attached to a spring that is fastened to a wall. The block is pulled to stretch the spring and then released. The distance, in inches, the block is from the wall for various times, in seconds, is given in the following table.

   Time (seconds)	0	1	2	3	4	5	6	7	8	9	10	11	12	13
   Distance (inches)	10.0	17.4	20.0	17.4	10.0	2.6	0.0	2.6	10.0	17.4	20.0	17.4	10.0	2.6

   Using inductive reasoning, what distance (in in.) will the block be from the wall after 14 seconds?
5. Give a counterexample to the given statement. A figure with four equal sides is a square.

6. Each of four siblings (Anita, Tony, Maria, and Jose) is given $5,000 to invest in the stock market. Each chooses a different stock. One chooses a utility stock, another an automotive stock, another a technology stock, and the other an oil stock. From the following clues, determine which sibling bought which stock.

   Anita and the owner of the utility stock purchased their shares through an online brokerage, whereas Tony and the owner of the automotive stock did not. The gain in value of Maria's stock is twice the gain in value of the automotive stock. The technology stock is traded on NASDAQ, whereas the stock that Tony bought is traded on the New York Stock Exchange.

   7. 

   The following graph shows the value of an original investment of $5,000 at the end of a year for 5 years. (See Example 3 in this section.)

   

   • A bar graph has years on the horizontal axis and "Value (in dollars)" on the vertical axis.
   • In year 1 the height of the bar is 5,250.00.
   • In year 2 the height of the bar is 5,512.50.
   • In year 3 the height of the bar is 5,788.13.
   • In year 4 the height of the bar is 6,077.53.
   • In year 5 the height of the bar is 6,381.41.

   Using induction, will the value of the investment at the end of year 6 be less than or more than $6,550?

   8. 

   The following table shows the number of grams of sugar that can be dissolved in water for various temperatures, in Celsius.

   Temperature	10	20	30	40	50	60
   Grams	10.03	11.2	12.47	13.89	15.45	17.19

   Using induction, will the number of grams of sugar that can be dissolved in water that is 70°C be less than or greater than 18 grams? (See Example 4 in this section.)

   9. 

   Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve the following exercise.

   There are 369 first-grade students in Park Elementary School. If there are 27 more girls than boys, how many girls are there?

   10. 

   Mensa is a society that welcomes people from every walk of life whose IQ is in the top 2% of the population. The following multiple-choice exercise is from a Mensa Workout.

   Following the pattern shown in the number sequence below, what is the missing number?

   1    8    27    ?    125    216