Grade 12 math: exponential & logarithmic function?

Dry cleaners use a cleaning fluid that is purified by evaporation and condensation after each cleaning cycle. Every time the fluid is purified, 2.1% of it is lost. The fluid has to be topped up when half of the original fluid remains. After how many cycles will the fluid need to be topped up?

Answer: 33 cycles

How do you solve this question?

Question

Grade 12 math: exponential & logarithmic function?

Dry cleaners use a cleaning fluid that is purified by evaporation and condensation after each cleaning cycle. Every time the fluid is purified, 2.1% of it is lost. The fluid has to be topped up when half of the original fluid remains. After how many cycles will the fluid need to be topped up?

Answer: 33 cycles

How do you solve this question?

anonymous · Answer

losses 2.1% means multiply by .979

anonymous · Answer

it is like a compound interest problem, but different. sorry, but i dont really know

anonymous · Answer

each cycle so solve 
$$.979^x =\frac{1}{2}$$

anonymous · Answer

you have a choice.  you can use logs, or you can just guess and check  but obviously you are supposed to use logs so lets do it

anonymous · Answer

$$.979^x=.5$$
$$x\ln(.979)=\ln(.5)$$
$$x=\frac{\ln(.5)}{ln(.979)}$$

anonymous · Answer

close to 33

he66666 · Answer

But why is it .979? Shouldn't it be 99.979 since you do 100-0.021? :S

anonymous · Answer

hope it is clear that if you lose 2.1% you retain 97.9 percent

anonymous · Answer

oh wait. in math we use numbers not their percent form to compute with. 100% =1, 
2.1% =.021

anonymous · Answer

you should subtract .021 from 1 or subtract 2.1 from 100 and then convert to a decimal

he66666 · Answer

Oh okay. Thanks so much! :)

anonymous · Answer

welcome