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!
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