How many days will it be before there is exactly one gallon left at the end of day n?

Question

Assume NASA is able to recycle 90% of its water consumed each day on the space shuttle. Also assume that an astronaut starts with 10 gallons of water and uses 1 gallon per day

Answer 1

Each day 0.1 gallon is lost.

10 - 0.1d = 1

-0.1d = -9

0.1d = -9

d = 90

 

On the 90th day they have only one gallon left.

 

Or

It takes 10 days to consume a gallon (0.1/day)

To consume 9 gallons was take 9(10) or 90 days.