Question

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?


Every foot of the pipe removes 20% of the pollutant.
Every foot of the pipe removes 80% of the pollutant.
The original amount of pollutant present in the fuel was 80 tons.
The original amount of pollutant present in the fuel was 20 tons.

Answer 1

Answer: first option, Every foot of pipe removes 20% of the pollulant.

Explanation:

20% removal means that after passing every foot of clay pipe, 80% of pollulant remains = 80/100 = 0.8

Then the amount of pollulant left in the fuel after passing x feet will be A*0.8^x

f(x) = 10(0.8)^x

Initial amount, A => x = 0 => f(0) = 10 = A

After one foot: 10 - 0.2(10) = 10*0.8

After two feet: 10*0.8 - 10*0.8*0.2 = 10*0.8[1-0.2] = 10*0.8*0.8 = 10*0.8^2

After three feet: 10*0.8^3

After n passes: 10*0.8^n