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?
1st wk = 2s = 2^1.
2nd wk = 4s = 2^2.
3rd wk = 8s = 2^3.
4th wk = 16s = 2^4.
36th wk = 2^36 = 6.8719*10^10s.
t = 6.8719*10^10s * (1/3600)h/s,
t = 19.09 Million Hours.
To calculate the amount of homework in hours for week 36, we first need to calculate the total amount of homework for the 36-week school year, and then convert it to hours.
The pattern mentioned in the question is a doubling sequence, where the amount of homework doubles each week.
In this case, the first week begins with one second of homework. Following the doubling pattern, the second week will have 2 seconds, the third week will have 4 seconds, and so on.
To find the total amount of homework for the 36-week school year, we can use a formula for the sum of a doubling sequence:
Total amount of homework = first term * (2^number of terms - 1)
In this case, the first term is 1 (one second in the first week), and the number of terms is 36 (36 weeks in the school year). Plugging these values into the formula:
Total amount of homework = 1 * (2^36 - 1)
Now, we need to convert the total amount of homework from seconds to hours. Since there are 60 seconds in a minute and 60 minutes in an hour:
Total amount of homework (in hours) = Total amount of homework (in seconds) / (60 seconds * 60 minutes)
Now we can calculate the answer:
Total amount of homework (in seconds) = 1 * (2^36 - 1)
Total amount of homework (in hours) = (1 * (2^36 - 1)) / (60 * 60)
Calculating this, the answer is approximately 5368.74 hours (rounded to two decimal places).
Therefore, this plan would require approximately 5368.74 hours of homework in week 36.