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4. The population P(t) of certain bacteria culture in an environment over time t in minutes is modeled by the following ODE: P' +2tP

4. The population P(t) of certain bacteria culture in an environment over time t in minutes is modeled by the following ODE: P' +2tP = e- sin(3t) Suppose initially there are 5000 bacteria. (a) Find out the population at t 1 and t = 3 minute(s). Round your answer to 2 decimal places. (b) What will happen to this bacteria culture eventually? Explain your answer.

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