A chemical plant flushes a pesticide into a river that contains a molecule potentially harmful to people if the concentration is too high. The dangerous molecule breaks down gradually so that 90% of the amount is dissipated by the end of the week. Suppose D units of the molecule are discharged each week.
a) Find the number of units of the molecule in the river after n weeks.
for this I made a sequence {D, D+ 1/10D... etc} and formed a series of D(1/10)^n but im not sure where else to go with this
b) Estimate the amount of the molecule in the water supply after a long time.
For this I solved the sum of the series, and got 10D/9, again not sure what else to do
c) If the toxic level of the molecules is T units, how large an amount of the molecule can the plant discharge each week.
I am not really sure how to go about this. obviously they cant have T amount discharged, so would it be T - something?
thanks for any help
a) Find the number of units of the molecule in the river after n weeks.
for this I made a sequence {D, D+ 1/10D... etc} and formed a series of D(1/10)^n but im not sure where else to go with this
b) Estimate the amount of the molecule in the water supply after a long time.
For this I solved the sum of the series, and got 10D/9, again not sure what else to do
c) If the toxic level of the molecules is T units, how large an amount of the molecule can the plant discharge each week.
I am not really sure how to go about this. obviously they cant have T amount discharged, so would it be T - something?
thanks for any help