Non routine
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De Moivre predicted the date of his death by assuming he required 15 additional minutes of sleep each day starting from a date when he needed 8 hours of sleep. He predicted death would occur when his sleep requirement reached 24 hours. An equation was written to model this situation as an arithmetic sequence. It showed De Moivre lived 64 days from the starting date.
Non routine
- 1. NON-ROUTINE PROBLEM QUESTION 4 TINAGARAN A/L MAGIS PARAN (901117-04-5295) MUHAMMAD BIN RAZALI (900629-03-5213)
- 2. As he grew older, Abraham De Moivre (1667- 1754), a mathematician who helped in the development of probability, discovered one day that he had begun to require 15 minutes more sleep each day. Based on the assumption that he required 8 hours of sleep on date A and that from date A he had begun to require an additonal 15 minutes of sleep each day, he predicted when he would die. The predicted date of death was the day when he would require 24 hours of sleep. If this indeed happened, how many days did he live from date A?
- 4. STEP 1 UNDERSTAND THE PROBLEM De Moivre found that if he needed 8 hours of sleep on Monday, for example, then he needed 8 hours and 15 minutes of sleep on Tuesday, 8 hours and 30 minutes on Wednesday. If we assume his prediction to be correct, we are to determine how many days he live until he required 24 hours of sleep. The only other needed information is that there are 60 minutes in an hour.
- 5. STEP 2 DEVISING A PLAN Use the strategy to write an equation We recognize that the problem entails looking at an arithmetic sequence The difference in this case is 15 minutes, or 16/60 or ¼ of an hour. The 1st term in the sequence is 8 + 1/4 , and we need to know the number of the term which has value 24.
- 6. STEP 3 CARRYING OUT THE PLAN Number of term Term 1 8+¼ 2 8 + ¼ + ¼ = 8 + 2( ¼) 3 8 + ¼ + ¼ + ¼ = 8 + 3( ¼) . . . . . . n 8 + n(1/4) = 24
- 7. Hence, we need to do is solve the equation : 24 = 8 + n(1/4) 24 = 8 + n(1/4) we see that 8 plus some number is 24 16 = n(1/4) that number must be 16 4(16) = n 64 = n Answer : De Moivre can live 64 days
- 8. STEP 4 LOOKING BACK Using the strategy of write an equation, we found that De Moivre can live 64 days after date A