Question

6:49 PM Mon Apr 29 Introduction to Diffe...d Their Applications AA Farlow, Stanley J. 2. Decay Equation Solve the decay equation y ky by both separation of variables and the inte- grating factor method. 6. Interpretation of 1/k in the Decay Equation The reciprocal 1/k (which has units of time) of k that appears in the decay equation y-ky has a rough interpretation that it is the time required for the solution y(t) to fall two-thirds of the dis- tance from the initial value yo to 0. See Figure 2.11. Why does this claim have merit? Hint: Eval uate the solution of the initial-value problemy- -ky, y(O)-yo at t-1/k and approximate 1/e - 3. Half-Life Problem The time required for the solution y of the decay equation to be reduced from the initial value yo to one- half of yo is called the half-life th (a) Find the half-life th in terms of the constant k. (b)Show that if the solution of the decay equa- tion is some constant C at some ti then the 1/3 solution one half-life later will be C/2. 7. Radioactive Decay A certain radioactive mater- ial is known to decay at a rate proportional to the Initially, 100 grams of the sub- ears the mass decays to 75 grams. Find an expression for the mass of the material at any time. What is the 4. Doubling Time The time required for the initial value yo of the growth equation amount present. stance are present, but after 50 y to double in value is called the doubling time td. Find the doubling value of this equation in terms of the constant k. halflife of the material? 8. Determining Decay from Half-Life A certain radioactive substance has a half-life of 5 hours. 5. The Annuity Equation Solve the annuity Back to page 1498 164 of 1646 165 of 1646 22 pages left in this chapter

please do #3,4 and 7

Answer 1

3) ven -z て : Ce 2- 링o) CE "Zに .ZAo e ct

Hend helb thme le nd kt kt더

Abte bottenla sample decayed 千万claonof 100 50 0.06433 100e