(b) A radioactive substance with decay constant k is produced at a constant rate of a units of mass per unit of time, t. A differential equation describing the rate of change of the mass Q(t) of the substance present at time t can be derived as follows: Q' = rate of increase of Q - rate of decrease of Q (1) Now the rate of increase is the constant a, and Q is radioactive with decay constant k. The latter means that the rate of decrease is kQ. Following Eq.(1), we therefore have Q' = a-kQ. Rewriting this differential equation and imposing the initial condition Q(0)=Qo shows that is the solution to the initial value problem Q+kQ=a, Q(0) = Qo. Instruction: Solve this initial value problem by applying the integrating factor method, then find and interpret lim Q(t). tx

(b) A radioactive substance with decay constant k is produced at a constant rate of a units of mass per unit of time, t. A differential equation describing the rate of change of the mass Q(t) of the substance present at time t can be derived as follows: Q' = rate of increase of Q - rate of decrease of Q (1) Now the rate of increase is the constant a, and Q is radioactive with decay constant k. The latter means that the rate of decrease is kQ. Following Eq.(1), we therefore have Q' = a-kQ. Rewriting this differential equation and imposing the initial condition Q(0)=Qo shows that is the solution to the initial value problem Q+kQ=a, Q(0) = Qo. Instruction: Solve this initial value problem by applying the integrating factor method, then find and interpret lim Q(t). tx

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...

See similar textbooks