MATA32H3 Exam Solutions Fall 2018: Intermediate Value Theorem, Marginal Cost, Compound Interest

• School: UTSC
• Department: Mathematics
• Course: MATA32H3
• Professor: All

Document Summary

Logarithmic differentiation is useful for differentiating exponentials to bases other than e and also for differentiation long products with several factors. to. Remember to convert the percentage interest rate a decimal fraction , and to covert back to a percentage if required: the correct answer is a. Note u(1) = e2 and use logarithmic differentiation: (cid:64) (cid:11) (cid:12) x ln ln x (cid:12) (cid:11) ln u u (cid:99) u (cid:32) (cid:32) 2 xe (cid:11) (cid:12) x (cid:14) ln (cid:32) (cid:64) (cid:14) x (cid:62) 10 (cid:186) (cid:170) (cid:14) (cid:187)(cid:188) (cid:171)(cid:172) x u (cid:99)(cid:63) (cid:11) (cid:12) 2 e: the correct answer is d. Let r = a = (desired apr /100) and use s = p(1 + r)n with s and p common , so that they cancel out. Let n = number of compounding periods (number of 4 month periods). 3 (cid:183) (cid:184) (cid:185) for n. (p cancels out) . 15 (cid:124) n must be rounded up, so use n = 16.