1. ## Exponential Graphs

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

My issue is coming to understand why the function is f(x)=0.85^x. What's the reasoning behind subtracting .15 from the whole before beginning to travel?

2. ## RE: Exponential Graphs

Imagine that you have a long pipe to begin with. For each stage you are losing 15% of the impurities which means you have (1-0.15) remaining to go onto the next stage. At the next stage you no longer have all the impurities but the (1-0.15) from the previous stage, since another 15% or (1-0.15) is lost then (1-0.15)*(1-0.15) = (1-0.15)^2 remains.

This continues until you get to the xth stage where you will have (1-0.15)^(x-1) * (1-0.15) = (1-0.15)^x. As 1-0.15 = 0.85 you arrive at the answer you mentioned of 0.85^x.

You're not subtracting the 0.15 from the first stage if that makes sense, imagine the mixture has travelled 0 feet and thus there would be (1-0.15)^0 = 1, ie: no impurities have gone which is what we'd expect

Interestingly, due to the nature of exponential equations all of the impurities cannot be filtered out in this manner.

3. I got that! It has an asymptote at y=0. -very proud- Thank you.