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Unformatted text preview: MAT1332A - Calculus for the Life Sciences II - Fall 2009 Assignment 2 This assignment is worth a total of 50 points. Due on Tuesday, October 27, at the beginning of the lecture. Sorry, no late assignments will be accepted. Please write your answers neatly in complete and clear sentences. Explain your reasoning. Providing only an answer is not acceptable. Do staple your pages. (1) (a) [6 points] Check that N ( t ) = t 1 + ct is a solution of the differential equation dN dt = N 2 t 2 . Treat c as an unspecified constant. (b) [5 points] Use that N (1) =- 1 to find c . Then give the solution N ( t ) corresponding to this initial condition. (2) The rate at which a bacteria population multiplies is proportional to the instantaneous amount of bacteria present at any time. The mathematical model for this dynamics can be formulated as follows: db dt = kb, where b is a function in terms of the time t , b ( t ) is the number of bacteria at the time t , and k is a constant. The general solution of this autonomous differentialis a constant....
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- Fall '09