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MAT 275 Homework 03 Due : 11/7/15

Please show couple of steps and then use MS excel to get solution of 3) to 14) on Homework 03 by 11/7 before 11:59 PM.

(1) Three grams of a radioisotope decay in two years to 0.9g. Determine the half life T and the constant k.

(a) T = 1.2 years, k = 0.6

(b) T = 3 years, k = 0.5

(d) T = .5 years, k = 0.5

(e) None of these

(2) The room temperature in your office is 70 degree Fahrenheit. Experience has taught you that the temperature of a cup of coffee brought to your office will drop from 120 degree Fahrenheit to 100 degree Fahrenheit in 10 minutes. What should be the temperature of your cup of coffee if you want it to take 20 minutes before it drops to 100 degree Fahrenheit?

(a) 120 degree Fahrenheit approx

(b) 153 degree Fahrenheit approx

(d) 60 degree Fahrenheit approx

(e) None of these

(3) Use Euler Method with step size h = 0.1 to approximate the solution to the initial valued

problem, dy dx

= x √ y and y(1) = 4 at x = 1.4(Select the result that is closest to your

answer.)

(a) 4.2543

(b) 4.2

(d) 4

(4) Use Improved Euler Method with step size h = 0.1 to approximate the solution to the initial

valued problem, dy dx

= x √ y and y(1) = 4 at x = 1.4(Select the result that is closest to your

answer.)

(a) 4.935672

(b) 4.964133

(d) 5.123117

(5) Use Euler Method with a fixed step size and 4 steps to approximate the solution to the initial

valued problem, dy dx

= y and y(0) = 1 at x = 1.(Select the result that is closest to your answer.)

(a) 2

(b) 2.56578

(d) 2.441411

(6) Use Euler Method with a fixed step size and 8 steps to approximate the solution to the initial

valued problem, dy dx

= y and y(0) = 1 at x = 1.(Select the result that is closest to your answer.)

(a) 2

(b) 2.56578

(d) 2.441411

(7) Use Improved Euler Method with a fixed step size and 4 steps to approximate the solution

to the initial valued problem, dy dx

= y and y(0) = 1 at x = 1.(Select the result that is closest to your answer.)

(a) 2

(b) 2.6721443

(d) 2.7114162

(8) Use Euler’s method to find an approximation of the solution to the initial valued problem y′ = 1 + t sin(ty), y(0) = 0 at t = 1, in 10 steps.

(a) y(1) = 0.87940

(b) y(1) = 1.03115

(d) y(1) = 1.39651

(e) None of these.

(9) Use Euler’s method to find an approximation of the solution to the initial valued problem y′ = 1 + t sin(ty), y(0) = 0 at t = 1, in 20 steps.

(a) y(1) = 1.04923

(b) y(1) = 1.13568

(d) y(1) = 1.32463

(e) None of these.

(10) Use Improved Euler’s method to find an approximation of the solution tothe initial valued problem y′ = 1 + t sin(ty), y(0) = 0 at t = 1, in 5 steps.

(a) y(1) = 0.91055

(b) y(1) = 1.25761

(d) y(1) = 2.00385

(e) None of these.

(11) Use Improved Euler’s method to find an approximation of the solution to the initial valued problem y′ = 1 + t sin(ty), y(0) = 0 at t = 1, in 10 steps.

(a) y(1) = 1.07007

(b) y(1) = 1.25436

(d) y(1) = 1.66639

(e) y(1) = 1.86300

(f) None of these.

(12) Finding the approximation of the transcendental number ”e ” is equivalent to solving the initial value problem y′ = y, y(0) = 1. and then evaluating a solution at x = 1. Use Euler’s Method to approximate ”e” using step size of .1.

(a) y10 = 1.77156

(b) y10 = 1.94872

(d) y10 = 2.35795

(e) y10 = 2.59374

(f) None of these.

(13) Finding the approximation of the transcendental number ”e ” is equivalent to solving the initial value problem y′ = y, y(0) = 1. and then evaluating a solution at x = 1. Use Improved Euler’s Method to approximate ”e” using step size of .1.

(a) y10 = 2.22279

(b) y10 = 2.45618

(d) y10 = 2.99906

(e) y10 = 3.313964

(f) None of these.

(14) After doing problem 3-13, which method do you think is more accurate?

(a) Euler method

(b) Improved Euler method

(15) State whether the following statement is True or False: Increase in step size will increase the accuracy of the solution.

(a) True

(b) False