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Question 996757: Polluted water is passed through a series of filters. Each filter removes 59% of the remaining impurities. Initially the water contains impurities at a level of 400 parts per million (ppm). Determine a rule for the function g , that gives the remaining level of impurities, L , after the water has passed through a series of n filters.
G(n)=?????
Thanks!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! each filter removes 59% of the remaining impurities.
remaining level of impurity equals 41% of the original impurity.
example:
400 parts per million start with.
pass through filter once.
remove .59 * 400 = 235
remaining = .41 * 400 = 164
235 + 164 = 400.
you can use .41 as the factor for the remaining impurities.
400 * .41 = 164 * .41 = 67.24 * .41 = 27.5684
basically you have 400 * .41 * .41 * .41 which is the same as 400 * .41^3
400 * .41^3 = 27.5684.
this works for any number of times you pass though the filter.
g(n) = 400 * .41^n
when n = 3, g(3) = 400 * .41^3 = 27.5684.
you could have used any variable name, such as x, as well.
g(x) = 400 * .41^x
when x = 3, g(3) = 400 * .41^3 = 27.5684.
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