Help with Geometric Functions please

So
a. so 100-1/10 of 100 or 100-10=90
then second dose minus 10% or 90-9=81
third dose 81 minus 10%=81-8.1=72.9
fourth dose 72.9 minus 10% or 72.9-7.29=65.61

so after 4th dose only 65.61% are left

b. so to get it to 5% you do alot and find that it takes 27 tries to get the percent down to 5.2% and 28 doses to get it to 4.7%

2160ft^3 i think you could use a formala to you out with this in the future