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(a) e2 + 3eA, (b) xe²", (c) ¤/(1+ e"), (d) (e³ – 1)*. - 9 2 Natural logarithms

(a) e2 + 3eA, (b) xe²", (c) ¤/(1+ e"), (d) (e³ – 1)*. - 9 2 Natural logarithms

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Solve 9.1.4 a,b,c and d
Let x be a positive number. The natural logarithm of x is the logarithm to base e of x, where e is as in the last section. Using the definition of logarithms given in Section 4.4, 168 9.2 It is c percentage rate) is e" – 1, expressed as a percentage. > and £P becomes £Pe"T. In s years at a rate of interest r is given by V = PeT. the (9.5) FC to be an integer: see Exercise 9.1.2. from now is given by solving (9.5) for P, given V: the present value is P = Ve-rT. (9.6) The formulae (9.5) and (9.6) assume a constant interest rate r. Also, we have yet considered the continuous-discounting analogue of finding the present value of an income stream, which we did for annual discounting in Section 5.3. So there is a lo more to be said on this topic, but that will have to wait until Chapter 19. Exercises 9.1.1 Use a calculator to verify (a) e'e = e°, (b) e°/e = e®, (c) e-4 = 1//e, (d) (el5)4 = e°. 9.1.2 Find the value after 10 years of £500 compounded (a) annually, (b) monthly, (c) continuously, at an interest rate of 4% per annum. Comment. How do your answers change when the time period involved is 2, years? 9.1.3 Find the present value of £400 to be paid in 5 years time if it is discounted (a) annually, (b) monthly, (c) continuously, at a rate of 7% per annum. Comment. 9.1.4 Differentiate (a) e2 + 3e-A, (b) xe²", (c) ¤/(1+ e"), (d) (e3× – 1)ª. 9.2 Natural logarithms we see that e
Transcribed Image Text:Let x be a positive number. The natural logarithm of x is the logarithm to base e of x, where e is as in the last section. Using the definition of logarithms given in Section 4.4, 168 9.2 It is c percentage rate) is e" – 1, expressed as a percentage. > and £P becomes £Pe"T. In s years at a rate of interest r is given by V = PeT. the (9.5) FC to be an integer: see Exercise 9.1.2. from now is given by solving (9.5) for P, given V: the present value is P = Ve-rT. (9.6) The formulae (9.5) and (9.6) assume a constant interest rate r. Also, we have yet considered the continuous-discounting analogue of finding the present value of an income stream, which we did for annual discounting in Section 5.3. So there is a lo more to be said on this topic, but that will have to wait until Chapter 19. Exercises 9.1.1 Use a calculator to verify (a) e'e = e°, (b) e°/e = e®, (c) e-4 = 1//e, (d) (el5)4 = e°. 9.1.2 Find the value after 10 years of £500 compounded (a) annually, (b) monthly, (c) continuously, at an interest rate of 4% per annum. Comment. How do your answers change when the time period involved is 2, years? 9.1.3 Find the present value of £400 to be paid in 5 years time if it is discounted (a) annually, (b) monthly, (c) continuously, at a rate of 7% per annum. Comment. 9.1.4 Differentiate (a) e2 + 3e-A, (b) xe²", (c) ¤/(1+ e"), (d) (e3× – 1)ª. 9.2 Natural logarithms we see that e
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