Question 1020588
The remaining amount of water in the swimming pool is modeled by the geometric expression 

{{{10^6(1-0.07)^x}}}, or {{{10^6*0.93^x}}}.

We want this expression to be less than or equal to 10% of 1,000,000, or 10^6, gallons of water, which is 10^5 gallons.  Hence

{{{10^6*0.93^x<=10^5}}}
==> {{{0.93^x <= 0.10}}}

Applying logs (base 10) to both sides, we get 

{{{x*log0.93 <= log0.10}}}
==> {{{x >= -1/log0.93 = 31.73}}} (the direction of the inequality is reversed because log0.93 is negative.)

Therefore on and after 31.73 days, there is 10% or less water remaining in the pool.