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Chapter 6: Q. 20 (page 556)
The mass of an object with density grams per cubic centimeter in the shape of a cone with radius meters and height meter.
The mass of the object is
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Suppose a population P(t) of animals on a small island grows according to a logistic model of the form for some constant .
(a) What is the carrying capacity of the island under this model?
(b) Given that the population is growing and that , is the constant k positive or negative, and why?
(c) Explain why for small values of .
(d) Explain why for values of that are close to the carrying capacity
find an equation that gives y as an implicit function of x. Then draw the continuous curve that satisfies this differential equation and passes through the point (2, 0).
Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52.
32.
Explain how equality is relevant to Euler鈥檚 method.
Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
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