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Hello everyone!
I am doing the following question:
The rate of decrease in the concentration of the drug in the bloodstream at time t hours is proportional to the amount x (mg) in the bloodstream at that time.
a) Show that , where k is a positive constant and is the size of the dose.
Ok, I did this part.
Then comes the difficult part.
b) Show that the amount of the drug in the bloodstream will never exceed
I did this
in the beginning of T=1
the amount of drug is
in the beginning of T=2
the amount of drug is
Then I thought that this could be the sum of an infinite geometric progression. So the sum would approach the limit
, but I'm missing the T!
Where am I going wrong?