Letter to a Friend 1. The function r = f (t) = 5 20 t + 2 , 1 t 12, gives the rate (in gal/min) at which water flows into a tank at time t minutes past noon (a negative rate means that water flows out of the tank). (a) Give a brief (one paragraph) interpretation of the integral 8 1 f (t) dt as it applies here. Focus on the meaning of the integral sign, the differential dt and the product f (t) dt. Include a sketch to supplement your interpretation as a signed area. (b) Use your description from part (a) to explain to a friend in Math 151 how to evaluate the integral without referring to either part of the Fundamental Theorem. Evaluate the integral in the course of your explanation. The idea here is to explain why the Fundamental Theorem works in this particular context. One or two paragraphs should suffice.

Letter to a Friend 1. The function 20 r = f(t) =5 - t+ 2 ' , -1