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Question: (a) On the slope field for dP/dt = 3P - 3P2 in Figure, sketch three solution curves showing different types of behavior for the population, P.
(b) Is there a stable value of the population? If so, what is it?
(c) Describe the meaning of the shape of the solution curves for the population: Where is P increasing? Decreasing? What happens in the long run? Are there any inflection points? Where? What do they mean for the population?
(d) Sketch a graph of dP /dt against P. Where is dP /dt positive? Negative? Zero? Maximum? How do your observations about dP /dt explain the shapes of your solution curves?
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Find the level of production that will maximize revenue. If the producer s costs are given by C(x) = 2 + 3x what should his level of production be to maximize.
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an empty water tank is being filled by a pump. after 2 mins the tank contains 125 gallons. if the volume of water in the tank varies directly as the time the water is pumped, find k and rewrite an equation to show the relationship.
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explain in your own words the difference between zero divided by seven and seven divided by zero. show a way of writing
Henry received a 6% raise. If his old monthly salary was $2,250, what is his monthly salary now? (Hint: Find the amount of the raise. The add the raise to the previous monthly salary.)
Sketch a graph of the following functions: g(x) = |2x2 - x -15|. Specify whether each function is even , odd, or neither. Write down the intervals in which each function is increasing
A two digit number is such that the product of its digits is 35. When 18 is added to the number, the digits interchange their places. Find the number.
a cowboy at a ranch fills a water trough that is 1.1 m long 68 cm wide and 44 cm deep. he uses a hose having a diameter
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