Question

a tank of water is contaminated with 60 pounds of salt in order to bring the salt concetration down to a level consistents with epa standards clean water is being piped into a tank and the well mixed overflow is being collected for removal to a toxic waste site. the result is that at the end of each hour there is 22percent less salt in the tank than at the beginning of the hour. Let S=S(t) denote the number of pounds of salt in the tank t hours after the flushing process begins.
A. explain why S is an exponential function and find its hourly factor
B. give a formula for S
C. make a graph of s

Answer 1

ds/dt = -0.22s

Answer 2

seperate, integrate , and you will get s = Ae^(-0.22t)

Answer 3

we know the initial value , when t=0 , s= 60 , that gives A=60

Answer 4

s = 60e^(-0.22t)

exponential decay ( very similar to e^(-x) ) except it has y intercept of 60 , and if we want the model to be realistic then you should only consider time greater than or equal to zero

so only graph the section of it where t>=0