question number 11

I've gotten a little bit behind on my blog posts ,so i am posting the solutions to two sequences questions from the handout (#11 and 15).

11. Scientists have determined that 8 parts per million (ppm) of oil in water is an acceptable level. After an oil spill, the level of oil in a spill zone rises to 900ppm. Its is known that each week the spilled oil is reduced by 40%.

a) How many weeks will it take for the oil to be at an acceptable level?

week 0- 900ppm of oil in water x 60% retention rate of oil in water (40% depletion rate)
week 1 - 540 x .6
week 2 - 324 x .6
week 3 - 194.4
week 4 - 116.64
week 5 - 69.984
week 6 - 41.99
week 7 - 25.194
week 8 - 15.117
week 9 - 9.07
week 10 - 5.442 ppm of oil

It would take 10 weeks for the oil to be at an acceptable level.

* I came about this answer by entering the formula 900* .6 on the homescreen of my calculator and pressing enter consecutively

b)Chemicals could be added to the spill zone at the beginning of each week to speed up the process. There are two treatments available:
Treatment 1 oil is reduced by an additional 50 ppm at a cost of $1 million per treatment

Treatment2 oil is reduced by an additional 10 ppm at a cost of $550 000 per treatment

Compare treatment 1 and 2 in order to recommend a treatment, if any. Analyze the cost and time required for each treatment. Support your answer by providing cost and time.

Treatment 1 Treatment 2

week 0 - 900 x 54.4% ( 45.6 removal rate) week 0 - 900 x 58.9% (41.1 % removal rate)
week 1 - 489.6 week 1 - 530
week 2- 266.342 week 2 - 312.229
week 3 - 144.89 week 3 - 183.903
week4 - 78.82 week 4 - 108.319
week 5 - 42.878 week 5 - 63.8
week 6 - 23.326 week 6 - 37.578
week 7 - 12.689 week 7 - 22.664
week 8 - 6.903 week 8- 13.037
week 9 - 7.679

I would recommend neither treatment, on account that one would have to double any of each treatment to have any greater effect on the amount of time that it takes for the oil to dissipate from the water, and doubling either of the treatments would have a tremendously significant dollar value.