City water, which is slightly chlorinated, is being used to flush a tank of heavily chlorinated water. The concentration C = C(t) of the chlorine in the tank t hours after flushing begins is given by the following formula.
C = 0.3 + 2.79e-0.33t milligrams per gallon
(a) What is the initial concentration of chlorine in the tank? ________________________________________________
mg/gal (b) Express the concentration of chlorine in the tank after 2 hours using functional notation.
Calculate the concertraction of chlorine in the tank after 2 hours. (Round your answer to two decimal places.
Hi there! Thank you for the opportunity to help you with your question!
We have a concentration C (measured in mg/gal), which depends on time, t (measured in hours), given by the exponential function
(a) When we ask for the initial concentration, we are asking for the moment when t=0. If you plug in t = 0 to that equation you get:
And since e^0 = 1, then
C(0) = 3.09 mg/gal
(b) For part b, we are asked to calculate the function when t=2, in functional form. That is, we need to replace the argument t, of the function, by the value we want to evaluate, in this case 2. (This is similar to how I used 0 as the argument of C(0) in the part a)
So the functional part is simply the lefthand side:
(c) Now, in order to calculate the value numerically, we need to plug in 2 whenever we see t in the right hand side:
Evaluating that numerically, to two decimal places is 1.74 mg/gal
Please let me know if you need any clarification. Always glad to help!
Aug 28th, 2015
Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.