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Sagot :
With regards to the function model then the true statement as per first and second derivatives is: (C)[tex]\frac{dw}{dt} = \frac{1}{100} W (70-W)[/tex], because the carrying capacity is 70 and the rate of change of the weight is 6 grams per hour when the weight is 10 grams.
When, W = 10 then [tex]\frac{dw}{dt}[/tex] = 6
When W = 35 then [tex]\frac{d_{2}w}{d_{2}t}[/tex] = 0
where the point influx occurs, the weight of the carrying capacity is half
Therefore, 35 = [tex]\frac{a}{2}[/tex]
Then the carrying capacity (a) = 35 x 2
a = 70
A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable. Calculus's core tool is the derivative. It is a crucial idea that is incredibly helpful in a variety of contexts: in daily life, the derivative can inform you how fast you are driving or assist you in predicting stock market changes; in machine learning, derivatives are crucial for function optimization.
Note that the full question is:
The weight, in grams, of a population of bacteria at time hours is modeled by the function, the solution to a logistic differential equation. Selected values of and its first and second derivatives are shown in the table above. Which of the following statements is true?
(A)[tex]\frac{dw}{dt} = \frac{35}{125} W (35-W)[/tex], because the carrying capacity is 35 and the rate of change of the weight is6 grams per hour when the weight is 10 grams.
(B)[tex]\frac{dw}{dt} = \frac{35}{250} W (35-W)[/tex], because the carrying capacity is 35 and the rate of change of the weight is3 grams per hour when the weight is 10 grams.
(C)[tex]\frac{dw}{dt} = \frac{1}{100} W (70-W)[/tex], because the carrying capacity is 70 and the rate of change of the weight is6 grams per hour when the weight is 10 grams.
(D)[tex]\frac{dw}{dt} = \frac{1}{200} W (70-W)[/tex], because the carrying capacity is 70 and the rate of change of the weight is3 grams per hour when the weight is 10 grams.
To learn more about derivatives: https://brainly.com/question/23819325
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