Spraying 18.0 mg of lysol will kill 80% of bacteria on the table. How much lysol must be sprayed to kill 95% of these bacteria on the table. (it will have an exponential relationsip)
If you spray 18mg, there are 20% of the bacteria remaining. If you spray another 18mg, it will kill all but 20% of the remaining bacteria, so there will be 20% * 20% = 4% remaining. Let r be the portion of bacteria remaining and x the amount of lysol sprayed. Then
r = (20%)^(x/18mg)
So we want to find the x that makes r=5%. As a check, since 36mg kills just a little too much, your answer should be slightly less than 36mg.
Post again in this thread if you're still having trouble.
Ok. Let r be the fraction of bacteria remaining, and let x be the amount of lysol sprayed. If you spray a very small amount, it will kill an amount of bacteria proportional to the fraction of bacteria remaining:
, where k is the constant of proportionality. Note the negative sign - as x increases, r decreases.
The solution is . Since not spraying any lysol results in no bacteria killed, r=1 when x=0, so C=1.
We also know that r=0.2 when x=18mg, so
So we want to know what x gives r=0.05.
or approximately 33.5mg.
It's essentially the same calculation as before.