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?
See:
http://www.jiskha.com/display.cgi?id=1302866384
To calculate the amount of homework in hours for week 36, we need to find the total number of seconds assigned for each week and then convert it to hours.
First, let's calculate the total seconds of homework assigned in week 36. We know that the homework doubles each week, so the pattern is as follows:
Week 1: 1 second
Week 2: 2 seconds
Week 3: 4 seconds
...
We can notice that the number of seconds doubles each week, which corresponds to a sequence of powers of 2: 2^0, 2^1, 2^2, and so on.
Week 36 corresponds to 2^(36-1) seconds of homework, as the doubling starts from 2^0 in the first week.
Calculating 2^(36-1) gives us 2^35 seconds of homework for week 36.
Now, let's convert this value to hours. There are 60 seconds in a minute, and 60 minutes in an hour. So to convert seconds to hours, we divide the total seconds by 60*60.
Total homework in hours for week 36 = (2^35) / (60*60)
Let's calculate this value: