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Please on paper Final Exam A - Page 7 of 10 Apr 21, 2023 4. The population P(t) of certain bacteria culture in an environment

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Final Exam A - Page 7 of 10 Apr 21, 2023 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 cos(3t) Suppose initially there are 3000 bacteria. (a) Find out the population at { = 1 and ( = 3 minute(s). Round your answer to 2 decimal places. (b) What will happen to this bacteria culture eventually? Explain your

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