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A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 9 hours there are 7,800 bacteria. When will the population.

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Presentation on theme: "A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 9 hours there are 7,800 bacteria. When will the population."— Presentation transcript:

1 A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 9 hours there are 7,800 bacteria. When will the population reach 31,000? Please round your answer to the nearest tenth. t=12.2 t=1.4 none of those t=47.4 t=3.4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2 Experiments show that if the chemical reaction {image} takes place at 45 {image} C, the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows: {image} How long will the reaction take to reduce the concentration of {image} to 30% of its original value? t = 1,204 none of those t = 1,166 t = 2,108 t = 1,018 t = 1,338 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3 A curve passes through the point ( 9, 9 ) and has the property that the slope of the curve at every point P is 3 times the y-coordinate P. What is the equation of the curve? {image} none of those 1. 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4 The rate of change of atmospheric pressure P with respect to altitude h is proportional to P provided that the temperature is constant. At 15 {image} C the pressure is kPa at sea level and 89.4 kPa at h = 910. What is the pressure at an altitude of 3,800 m? P = 27.9 kPa P = 58.8 kPa P = 66.8 kPa P = 61.5 kPa P = kPa none of those 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5 Consider a population P = P(t) with constant relative birth and death rates {image} and {image} , respectively, and a constant emigration rate m, where {image} and m = 0.7. Then the rate of change of the population at time t is modeled by the differential equation {image} where {image} . Find the solution of this equation with the rate of change of the population at time t = 3 that satisfies the initial condition P(0) = 3,000. 13,440.2 none of those 16,440.2 1,920.0 13,449.2 10,440.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

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