Afuel 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.

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

  remember that hf is only the energy of one photon. not two. not three. one.  1) 5.12 * 10^3 photons  find the energy of one photon, then determine how many photons are needed to reach the sensitivity.  e = hf  = (6.626 * 10^-34 js)(5.95 * 10^19 hz)  = 3.94247 * 10^-14 j per photon  (2.02 * 10^-10 j) / (3.94247 * 10^-14 j/photon) = 5123.69149 photons  round to three sig figs.  2) 5.77 * 10^-17 j  energy of pulse = energy per photon * number of photons  = hfn  = (6.626 * 10^-34 js)(1.66 * 10^13 hz)(5250)  = 5.774559 * 10^-17 j  round to three sig figs.  3) 4.07 * 10^8 kj/mol  10^12 pm = 1 m  c = fλ  f = c/λ  e = hf  = hc/λ  = [(6.626 * 10^-34 js)(3.00 * 10^8 m/s) / (2.94 * 10^-12 m)](1 kj/1000 j)(6.02 * 10^23 photons/mol)  = 40702571.4 kj/mol  round to three sig figs.  4) 9.94 * 10^-1 m  e = hc/λ  λ = hc / e  = (6.626 * 10^-34 js)(3.00 * 10^8 m/s) / (2.00 * 10^-25 j)  = 0.9939 m  round to three sig figs.  5) 9.06 * 10^3 photons  energy of pulse = energy per photon * number of photons  number of photons = energy of pulse / energy per photon  = energy of pulse / (hf)  = (3.87 * 10^-13 j) / [(6.626 * 10^-34 js)(6.45 * 10^16 hz)]  = 9055.23695 photons  round to three sig figs.  6) 2.78 * 10^-15 j  this is problem 1, except in reverse.  sensitivity = minumum number of photons * energy per photon  = (5930)(6.626 * 10^-34 js)(7.077 * 10^14 hz)  = 2.78070758 × 10^-15 j  round to three sig figs.