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1. The population P(t) of certain bacteria culture in an environment over time f in minutes is modeled by the following ODE: P 4+ 2t

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1. The population P(t) of certain bacteria culture in an environment over time f in minutes is modeled by the following ODE: P 4+ 2t P - e sin (3t) Suppose initially there are 5000 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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