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Population models The population of a culture of bacteria has a growth rate given by
- a. Using the population model with r = 2, what is the increase in the population over the time interval 0 ≤ t ≤ 4?
- b. Using the population model with r = 3, what is the increase in the population over the time interval 0 ≤ t ≤ 6?
- c. Let ΔP be the increase in the population over a fixed time interval [0, T]. For fixed T, does ΔP increase or decrease with the parameter r? Explain.
- d. A lab technician measures an increase in the population of 350 bacteria over the 10-hr period [0, 10]. Estimate the value of r that best fits this data point.
- e. Looking ahead: Use the population model in part (b) to find the increase in population over the time interval [0, T], for any T > 0. If the culture is allowed to grow indefinitely (T → ∞), does the bacteria population increase without bound? Or does it approach a finite limit?
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