MATH 0290 Midterm: Math 0290 Exam 1 (0290) 2016 Sping Solution -191
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S o l u t i o n s: (15 points) a hospital received 200 mg of the isotope iodine 131. Let n (t) be the number of remaining nuclei after time t. N = n , n (0) = 200. To nd (or e ) we use the condition n (14) = 60. So, we get n (t) = 200(. 3)t/14 (cid:0)= 200et ln(0. 3)/14(cid:1) Then n (t ) = 100 or 200(. 3)t /14 = 100, (. 3)t /14 = . 5, t. Hence t = 14 ln(. 5) ln(. 3) days: (15 points) determine a type of the given di erential equation and nd the solution of the initial value problem. (3 + t)x + x = sin t, x(0) = 0. Solution: divide both sides by 3 + t to get a rst order linear di erential equation: x + (3 + t) 1 x = (3 + t) 1 sin t.
