Autonomous differential Equation
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The rate at which a bacteria population multiplies is proportional to
the instantaneous amount of bacteria present at any time. The mathematical model for this dynamics can be formulated as follows:
db/dt = kb
where b is a function in terms of the time t, b(t) is the number of bacteria at the time t, and k is a constant. The general solution of this autonomous dierential equation is
b(t) = b(0)e^(kt)
(a) Given that the initial population size b(0) doubles in two hours, f nd k. (Hint: use the logarithmic function)
(b) Find b(t) in terms of b(0) using the value of k found in (a). Simplify your answer by using the power properties of the exponential
function. Your nal answer should involve neither ln, nor e.
(c) Use (b) to answer the following question: in how many hours
will the bacteria population quadruple, that is, be four times the original population b(0)?
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Autonomous differential equation is solved.
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The rate at which a bacteria population multiplies is proportional to
the instantaneous amount of bacteria present at any time. The mathematical model for this dynamics can be formulated as follows:
db/dt = kb
where b is a function in terms of the time t, b(t) is the number of bacteria at the time t, and k is a constant. The general solution of this autonomous dierential equation is
b(t) = b(0)e^(kt)
(a) Given that the initial population size ...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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