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Massachusetts Institute of Technology Harvard-MIT Division of Health Sciences and Technology and Department of Electrical Engineering and Computer Science HST.410J/6.07J Projects in Microscale Engineering for the Life Sciences Homework Assignment #1 Issued: February 8, 2007 Due: February 15, 2007 Problem 1. Consider an exponential function of time, x ( t ) = Ae t/� + B. Part a. We can approximate this function at t = 0 by a straight line that passes through x (0) with a slope equal to the slope of the exponential function. We can also approximate this function as t � ± by a straight line through x ( ) with zero slope. Determine the time T where these two straight lines intersect. ± Part b. Determine the time constants a and b of the exponential functions shown by the solid curves in the following plot labelled “a” and “b,” respectively. Briefly explain your method. 3 0 –3 0 5 10 Part c. Determine the time constant c of the exponential function shown by the solid curve in the previous plot labelled “c.” Briefly explain your method. Problem 2. Estimate the velocity with which fluid flows through your microfluidic chamber.
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