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MATH 101 HOMEWORK 10 Due on Wednesday Dec. 1, 2004. For full credit, show all work. Calculators are not allowed, except as indicated below. 1. (5 marks) A bank determines that the waiting time for a customer’s call to be answered by a representative is modelled by an exponential density function whose expectation k depends on the number of representatives they employ. If the bank wants 90% of the calls to be answered within the first 7 minutes, what value of k should it aim for? (You may use a calculator to finish the computations.) 2. (10 marks) Solve the differential equations: (a) y 0 = 1+x , y(1) = −4, xy (b) xy 0 − 3y = x4 cos x. 3. (5 marks) End of term: everyone gets 5 marks for free! This homework covers Sections 7.8 and 7.9. Additional recommended exercises: Section 7.9: 1–16. 1