The decay of 200 particles of a particular radioactive substance is given by y=200(0.93)^x, where x is the number of days and y is the number of particles remaining. It costs the laboratory $1.50 per day to store each particle. On which day will the cost to store the particles be $135.

Question

The decay of 200 particles of a particular radioactive substance is given by y=200(0.93)^x,  where x is the number of days and y is the number of particles remaining. It costs the laboratory $1.50 per day to store each particle. On which day will the cost to store the particles be $135.

a) day 4
b) day 11
c) day 9
d) day 5

Anonymous · Answer

y = 135/1.50 = 90 particles 90 = 200 * .93^x 0.45 = .93^x log 0.45 = x log 0.93 -.347 = x * -.0315 x = 11

Anonymous · Answer

Lo and behold, 11 is an answer choice.