SOLUTION: To clean your room on a weekly basis, the first cleaning takes you 135 minutes. You notice that for each cleaning after that, you decrease the time it takes from the week before b

Question 447460: To clean your room on a weekly basis, the first cleaning takes you 135 minutes. You notice that for each cleaning after that, you decrease the time it takes from the week before by one-fifth.
In which week will it take you less than 15 minutes to clean your room?
How long will it take you in the 20th week to clean your room?

I think I use 135(4/5)^x but I'm not sure.
Thanks for your help.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
To clean your room on a weekly basis, the first cleaning takes you 135 minutes. You notice that for each cleaning after that, you decrease the time it takes from the week before by one-fifth.
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T(x) = 135(4/5)^(x-1) where x is the # of the week
In which week will it take you less than 15 minutes to clean your room?
Solve: 135(4/5)^(x-1) < 15
(4/5)^(x-1) = 0.11111..
(x-1)*log(4/5) = log(0.1111)
--
x-1 = log(0.111111..)/log(4/5) = 9.8467
x = 10.8467
In the 11th week
============================================
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How long will it take you in the 20th week to clean your room?
Solve:
T(20) = 135(4/5)(19) = 1.95 minutes
=========================================
Cheers,
Stan H.
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