Question

I need help on Number Three ONLY. Thank You!

1. Find the general solution to the ODE: y = tye-l, where t > 0. What is the limit fort → of y(t)? 2. Solve the initial Value Problem: y = y2, y) = yo, with yo ER. Does the solution exist for all tER? 3. The Kennewick Man skeleton was found on a bank of the Columbia River near Kennewick, WA on July 28, 1996. It was determined that the bones contain about 43% less C- 14 (half-life 5730 years) than it did when he died. The quantity of C-14 at time t satisfies the ODE: ' (t) = k e(t), with k < 0. How old is the Kennewick Man? (Hint: start by computing the decay rate k).

Answer 1

(3) Aol Gven 9uantity of C-14 at time t Satis fieaf a'rt)= KBrt) d& k& dt d& Kdt er Aekt halt hate 5730 Yean le. at t-0, &= o and t-5730, 8 o at Thus, A 80 5730. K Ae and 5730 K 5730 K= lo) 5B0

28 /1996. Now on E was determined that bones lontain about 43% less C-14 This man that time 577 C-14 ane at Psesent in skelbn hen at that time &=5780 10D So &=6pekt K = 5730 ) ekt- 570 e tt Kt = 10 Foom table 5730. t = K t 5730 X 0.81 4646 yean (ApP) Kennewick man one 4646 7ean old