A Science instrutor assigns his student one second of home work..the first week of school,two seconds. the second week four seconds, the third.if the student asked whether he would agree to this weekly homework doubling for the duration of the 36-week school year.how much homework in hours would this plan require in week 36?
Make a list:
week time cumulative time(seconds)
1....1........1
2....2........3
3....4........7
4....8.......15
5...16.......31
6...32.......63
.......
10..512.....1023
....
20.524288...1048575
....
If you check the numbers, you will find that the number of seconds of homework for week "n" is 2^(n-1).
With a calculator in hand, it won't be long for you to find out that after the 16th week, the student will spend the whole week, day and night, doing homework.
Additional help throughout the 36 weeks.Thanks!
You're welcome any time, 36 weeks or not!
To find out how much homework in hours would be required in week 36, we need to calculate the total amount of homework assigned for each week and then convert it to hours.
From the given information, we can see that the homework doubles each week. So, we can establish the following pattern:
Week 1: 1 second
Week 2: 2 seconds
Week 3: 4 seconds
...
This can be represented as a geometric sequence, where the common ratio is 2 (each week doubles the previous week's homework).
To find the total amount of homework assigned in week 36, we can use the formula for the sum of a geometric sequence:
Sn = a * (r^n - 1) / (r - 1)
Where:
Sn is the sum of the series
a is the first term of the series
r is the common ratio of the series
n is the number of terms in the series
In this case:
a = 1 (the first week's homework)
r = 2 (doubling factor)
n = 36 (number of weeks)
Substituting these values into the formula:
Sn = 1 * (2^36 - 1) / (2 - 1)
Simplifying the expression:
Sn = (2^36 - 1)
Calculating the value of 2^36 gives us:
Sn ≈ 68,719,476,735
Therefore, the total amount of homework assigned in week 36 would be approximately 68,719,476,735 seconds.
To convert this to hours, we need to divide by the number of seconds in an hour. There are 3,600 seconds in an hour.
Total homework in hours = 68,719,476,735 seconds / 3,600 seconds/hour
Calculating this value gives us:
Total homework in hours ≈ 19,088,743 hours
So, this plan would require approximately 19,088,743 hours of homework in week 36.