maths investigation: a new dry cleaning machine has been designed following completion of each cleaning cycle the new dry cleaning liquid will be purified by evaporation and 2% of the liquid will be lost develop a formula that used indices to determine the amount of liquid left after N uses. show that after 20 uses the quantity of liquid remaining is approximately two thirds of the original quantity (1000 mL)

Question

maths investigation: a new dry cleaning machine has been designed following completion of each cleaning cycle the new dry cleaning liquid will be purified by evaporation and 2% of the liquid will be lost develop a formula that used indices to determine the amount of liquid left after N uses. show that after 20 uses the quantity of liquid remaining is approximately  two thirds of the original quantity (1000 mL)

anonymous · Answer

If 2% is lost after each cycle, then following each cycle we are left with 0.98 of what we had before. The original amount of liquid is 1000, so after N uses we are left with $1000(0.98)^N$ of the original quantity.
Check: after 20 uses we have $1000(0.98)^20=667.6\approx \text{two thirds of original.}$

anonymous · Answer

Does this make sense? It's kind of similar to the compound interest formula.

anonymous · Answer

thank you! this has helped a lot! i understand it now :)