At a given level of effort, it is reasonable to assume that the rate at which fish are caught depends on the population y: the more fish there are, the easier it is to catch them. thus we assume that the rate at which fish are caught is given by ey, where e is a positive constant, with units of 1/time, that measures the total effort made to harvest the given species of fish. to include this effect, the logistic equation is replaced by dy/dt = r(1 − y/k)y − ey. (i) this equation is known as the schaefer model after the biologist m. b. schaefer, who applied it to fish populations. (a) show that if e < r, then there are two equilibrium points, y1 = 0 and y2 = k(1 − e/r) > 0. (b) show that y = y1 is unstable and y = y2 is asymptotically stable.

Astudent looks at ocean waves coming into the beach. an ocean wave with more energy will a) have a greater height. b) have a greater period. c) travel toward the beach faster. d) strike the beach with greater frequency.

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

How is sound energy produced a. vibrating objects b. objects being heated c. temperature differences d. stationary objects