The number of bacteria present in a Petri dish can be modeled by the function N=50 e^{3 t}, where N is the number of bacteria present in the Petri dish after t hours. Using this model, determine, to the nearest hundredth, the number of hours it will take for N to reach 30,700 .

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Accepted Answer

Step:1 ：Solve the equation (30,700 = 50 e^{3t}) for (t)Step:2 ：Calculate (t) using the equation (t = frac{ln(frac{30,700}{50})}{3})Step:3 ：Simplify the final answer: (t approx 2.14)Step:4 ：(boxed{2.14}) hours

Answer

Step: 1 ：Solve the equation (30,700 = 50 e^{3t}) for (t)Step: 2 ：Calculate (t) using the equation (t = frac{ln(frac{30,700}{50})}{3})Step: 3 ：Simplify the final answer: (t approx 2.14)Step: 4 ：(boxed{2.14}) hours

The number of bacteria present in a Petri dish can be modeled by the function $N=50 e^{3 t}$, where $N$ is the number of bacteria present in the Petri dish after $t$ hours. Using this model, determine, to the nearest hundredth, the number of hours it will take for $N$ to reach 30,700 .

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