100 g of a substance is left to evaporate. Each day it loses one-tenth of its weight at the beginning of the day. How many days elapse before it is less than half its orignal mass?

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justaguide eNotes educator| Certified Educator

100 g of a substance is left to evaporate. Each day it loses one-tenth of its weight at the beginning of the day.

The mass of the substance at the end of day 1 is 100*(1 - 1/10). The mass of the substance at the end of N days is 100*(1 - 1/10)^N.

To determine the number of days that elapse before it is less than half its original mass, solve the equation `100*(1 - 1/10)^N = 50` for N

=> `(1 - 1/10)^N = 0.5`

Take the log of both the sides

N = `(log 0.5)/(log 0.9)`

= `N ~~ 6.57`

The number of days that elapse before it is half its original mass is 6