### Answer to sTEm-at-work Puzzle #59: Miniature implanted pump performance

Analysis: The pump is performing as expected if it uses 0.70 Joules during the 3.5 second test period. The actual puzzle answer requires the student to understand that the total energy value is the area under the curve from 0 to 3.5 seconds. This then allows for (a) simple linear integration formula practice or (b) reinforcement of the area approximation method for determining the area under the response data. For students with introductory calculus skills (a) the area can be determined as the integration results (sum) of the 4 linear equations between 0 seconds and 3.5 seconds.

In the area approximation case (b), area under the curve above the 0.2 joules/second horizontal between 1.5 seconds and 2.5 seconds is approximately matched by same amount of area below that horizontal between 2.5 seconds and 3.5 seconds. This leads to the construction of a rectangle that is 3.5 seconds by 0.2 joules/ second with a 0.70 Joule (0.20 j/s x 3.5 sec) area. Either method (a) or (b) leads to 0 .70 joules as the energy value which is the value expected for a good pump.

Question: Does pump DP-3ml meet test criteria? YES or NO?