Question

Question #a6757

Answer 1

`17.8%`

Your specific questions are answered in bold

Explanation:

Let’s figure out how much water is lost first then we can figure out how much water is left in the tank.

Since the amount of water lost is 10% more each day, the series is geometric, meaning we must use the following formula:

`S_n=(a_1(1-r^n))/(1-r)` where `a_1=10` and `r=1.1`

(1)`r=1.1` because every day your water loss increases 10 % more than what you lost on the previous day (in other words `110%` of the previous day). For example, on day 1 you lose 10 liters, on day 2 you lose `1.1(10)=11` liters.

So our formula to find `S_30` is:

`S_30=(10(1-1.1^30))/(1-1.1)=(10(1-1.1^30))/(-.1)=-100(1-1.1^30)`
`=-100(-16.4494)=1644.94` liters

By subtracting this number from 2000 we can figure out how many liters are left:
`2000-1644.94=355.06` liters

Dividing this number by 2000 gives us the percent remaining: `17.8%`

(2)I am not sure what formula you are referring to, but this is pretty standard for geometric series.

(3)Notice that my answer got the same number as the answer online. The person you got the answers from simply switched the terms in the top and bottom to avoid the double negatives that eventually divide away anyway.