SOLUTION: The earliest mechanical clock appeared around 1350 in europe and would gain or lose and average of 30 minutes per day. After that, accuracy roughly doubled every 30 years. find the

Question 569105: The earliest mechanical clock appeared around 1350 in europe and would gain or lose and average of 30 minutes per day. After that, accuracy roughly doubled every 30 years. find the predicted accuracy of the clock in the years 1700 and 2000.
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The earliest mechanical clock appeared around 1350 in europe and would gain or lose and average of 30 minutes per day. After that, accuracy roughly doubled every 30 years. find the predicted accuracy of the clock in the years 1700 and 2000.
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"accuracy...doubled..." is not a good term. If the accuracy is 10%, then double that is 20% ??
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If you mean the error was reduced by a factor of 2:
1350 - 1700 = 350 yrs
350/30 =~ 12 periods
30 mins error * (1/2)^12 = 30/1024 =~ 0.03 min/day = 1.8 seconds/day
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1350 - 2000 = 650 yrs = 22.7 periods
30 min*(1/2)^22.7 =~ 4.403E-6 min/day
=~ 264 microseconds/day

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If is the time gained or lost the 1st year,
After 30 yrs:

Next 30 yrs:

Next 30 yrs:

----------
So, at the end of yrs,
The accuracy is
If

min/day
min/day
You can use log to solve this. Call it
for accuracy

When you find , then

( I don't have calculator handy )
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