Question

(04.07) A fuel is purified by passing it through a clay pipe. Each foot of the clay pipe removes a fixed percentage of impurities in the fuel. Let f(x) represent the amount of pollutants, in tons, left in the fuel after it had passed through x feet of the clay pipe: f(x) = 10(0.8)x What does the number 0.8 represent?

Answer 1

Answer: Every foot of the pipe keeps 80% of the pollutant.

Justification:

1) the function is f(x) = 10 * (0.8)^x

2)  That means that the amount of fuel, f(x), is multiplied by 0.8 every foot it passes.

Initially the amount of poluulants 10 tons.

After 1 foot the amount pollulants remaining  is 10 * 0.8 = 8 tons

That is (8/10)*100% = 80%.

3) You can to that same calculation in a general form to jusitfiy the result for every foot.

Suppose x = n

=> f(n) = 10 * (0.8)^n

=> x + 1 = n+1 => f(n+1) = 10 * (0.8)^(n+1)

Percent of pollulant remaining, % = [ f(n+1) / f(n)] * 100

=> % = { [10 * 0.8^(n+1) ] / [10 * 0.8^(n) ] } * 100 = 0.8^ (n+1-n) * 100 = 0.8^(1) * 100 = 0.8 * 100 = 80.

So, 80% of pollulant remains after every foot o fpipe.

Answer 2

The number 0.8 represents that every  foot of pipe removes 20% of the pollulant, leaving the 80% ( 80/100=0.80)