2. For a certain strain of bacteria, 𝑘 = 7.75 when 𝑡 is measured in hours.a. What is the doubling time of the bacteria?b. How long will it take 2 bacteria to increase to 1000?
Question
- For a certain strain of bacteria, 𝑘 = 7.75 when 𝑡 is measured in hours.a. What is the doubling time of the bacteria?b. How long will it take 2 bacteria to increase to 1000?
Solution
The question seems to be related to the exponential growth of bacteria, which can be modeled by the equation P(t) = P0 * e^(kt), where P(t) is the final population, P0 is the initial population, k is the rate of growth, and t is time.
a. The doubling time of the bacteria can be found by setting P(t) = 2*P0 and solving for t.
2*P0 = P0 * e^(kt) 2 = e^(kt) ln(2) = kt t = ln(2) / k t = 0.693 / 7.75 t ≈ 0.089 hours
So, the doubling time of the bacteria is approximately 0.089 hours.
b. To find out how long it will take for 2 bacteria to increase to 1000, we can set P0 = 2 and P(t) = 1000 in the equation and solve for t.
1000 = 2 * e^(7.75t) 500 = e^(7.75t) ln(500) = 7.75t t = ln(500) / 7.75 t ≈ 0.92 hours
So, it will take approximately 0.92 hours for 2 bacteria to increase to 1000.
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