Hello, community! This question is for all of those Calculus people out there.

The volume of a swimming pool is changing with respect to time, such that the volume is given by W(t), where W(t) is measured in cubic centimeters and t is measured in seconds. A tangent line is shown for W(t) at t = 3 seconds. Determine the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.
(I've narrowed down the answer choices to 2, and just really need to find the right way of thinking to find the answer)

(A) W(lim t) as t goes to 3.
(B) [W(3.1) - W(2.9)] / 0.2.

Thank you in advance!

Step-by-step explanation:

the rate of change is the slope of the line at the point you're interested in.   Also the rate of change is the derivative of the formula for the line.  if that makes sense?

that darker line is the linear approximation ( tangent)  for the slope of the line at the point of interest (3)  s,  I can see that the slope of the tangent line is a little less then 1/2  and if you are given the formula and use that with either of the ways to get the answer, then you'll find that  using the lim(t)  as t goes to 3 will be exact while the B answer would just be an approximation , but probably still quite close

Does that help ?  :/  

step-by-step explanation:

i believe its "c" because all of the other options include a but it could be d because there is a way of financing with cash at certain places but its uncommon.