Please help me with this problem?

Question

I am studying for my math final tomorrow and I need some help on this problem:

When kerosene is purified to make jet fuel, pollutants are removed by passing the kerosene through a special clay filter. Suppose a filter is fitted in a pipe so that 15% of the impurities are removed for every foot that the kerosene travels. Write and exponential function to model the percent of impurity left after the kerosene travels x feet.

Please also tell me why you got that answer.

Answer 1

.85^x

For each foot of the pipe 15% is removed so that leaves 85% or (.85)^1. As the kerosene travels another foot 85% of the 85% of impurities are left (.85)(.85). This can be expressed as a (.85)^2.

Answer 2

Its so late my brain is misfiring, but to help you with the English part of this...

if the filter is 1 foot the volume would be reduced by 15% of the impurities. So if you had 100 gallons at the start with 10% impurities, you would end up with 100 gallons with 8.5% impurities.

For the second foot, you start with a liquid that already is reduced to 8.5% impurities so the formula produce 100 gallons with 7.225% impurities.

Each foot after that continues to change the amount of impurities by 15%.
1 - 10.00%
2 - 8.50%
3 - 7.23%
4 - 6.14%
5 - 5.22%
6 - 4.44%

I don't think the volume of the liquid lessens, just the impurity percent. So you need a variable for the starting amount of impurities, the volume flowing through, and the number of feet of filter. Actually, now that I think about it, I don't think the volume really matters in the formula... you need to come up with something to multiply any volume by to get the purity level. It seems really important to identify the starting impurity level though.

What I am saying is if you had 100 gallons of liquid and tossed in a couple of handfuls dirt you wouldn't significantly change the volume of liquid, but you would impact the percent of impurity.

I would really try to give this more thought by I am a bit fried myself for the corporate world. I wish you the very best of luck on this test tomorrow and wish I could have been of more help.

There must be an argument for why you just wouldn't put in 8-10 feet of filter and go to zero, but the formula does not take into account things like how much the filter costs (what if it is $100,000 a foot?) or what the filter does to the flow (what if a 1-foot filter passes 100 gallons a minute and a 2-foot filter passes 50 gallons a minute and a 3-foot filter passes 25 gallons a minute). Also, there must be an upper limit when the filter no longer reduces 15%, because you can't get better than "pure".

Gosh I wish I was thinking clearer.

Answer 3

Your pipe will be clogged and be useless to go on further in the long run...