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.

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?

3. STRATEGY
Write an Equation

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