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The initial size of a bacteria culture is 1000. After one hour the bacteria count is 8000. After how many hours will the bacteria population reach 15000? Assume the population grows exponentially.

User Nyc
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Answer: Let’s assume that the bacteria population grows exponentially according to the formula P(t) = P0 * e^(kt), where P0 is the initial population, k is the growth rate, t is time in hours, and e is the mathematical constant approximately equal to 2.71828. We know that at time t = 0, the population is P(0) = 1000. After one hour, the population is P(1) = 8000. We can use this information to solve for the growth rate k. Substituting the values into the formula, we get: 8000 = 1000 * e^(k * 1) Dividing both sides by 1000, we get: 8 = e^k Taking the natural logarithm of both sides, we get: ln(8) = k Now that we have solved for k, we can use the formula to find out when the population will reach 15000. 15000 = 1000 * e^(ln(8) * t) Dividing both sides by 1000, we get: 15 = e^(ln(8) * t) Taking the natural logarithm of both sides, we get: ln(15) = ln(8) * t Dividing both sides by ln(8), we get: t = ln(15)/ln(8) ≈ 1.71 hours So it will take approximately 1.71 hours for the bacteria population to reach 15000. Received message.

User Liad
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