I need help more of an explanation than the answer.

Mathematics
Tutor: None Selected Time limit: 1 Day

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.
C(                   )

 Calculate the concertraction of chlorine in the tank after 2 hours. (Round your answer to two decimal places.

Aug 28th, 2015

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(2)

(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

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Aug 28th, 2015
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Aug 28th, 2015
May 22nd, 2017
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