Concept explainers
Learning Curve Psychologists sometimes use the function
to measure the amount
Determine the rate of learning
Approximately how many words will the student have learned after
After
How long does it take for the student to learn
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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Flood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forwardradioactive Decay These exercises use the population radioactive Decay. Radioactive Radium The half life of radium 226 is 1600 years. Suppose we have a 22-mg sample. (a) Find a function m(t)=m02r/k that models mass remaining after t years. (b) Find a function m(t)=m0ert that models the remaining after t years. (c) How much of sample will remain after 4000 years? (d) After how many years Will only 18 mg Of sample remain?arrow_forwardGrazing Kangaroos The amount of vegetation eaten in a day by a grazing animal V of food available measured as biomass, in units such as pounds per acre. This relationship is called the functional response. If there is little vegetation available, the daily intake will be small, since the animal will have difficulty finding and eating the food. As the amount of food biomass increases, so does the daily intake. Clearly, though, there is a limit to the amount the animal will eat, regardless of the amount of food available. This maximum amount eaten is the satiation level. a.For the western grey kangaroo of Australia, the functional response is G=2.54.8e0.004V, where G=G(V) is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Draw a graph of G against V. Include vegetation biomass levels up to 2000 pounds per acre. ii. Is the graph you found in part i concave up or concave down? Explain in practical terms what your answer means about how this kangaroo feeds. iii. There is a minimal vegetation biomass level below which the western grey kangaroo will eat nothing. Another way of expressing this is to say that the animal cannot reduce the food biomass below this level. Find this minimal level. iv. Find the satiation level for the western grey kangaroo. b. For the red kangaroo of Australia, the functional response is R=1.91.9e0.033V, Where R is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Add the graph of R against V to the graph of G you drew in part a. ii. A simple measure of the grazing efficiency of an animal involves the minimal vegetation biomass level described above: The lower the minimal level for an animal, the more efficient it is at grazing. Which is more efficient at grazing, the western grey kangaroo or the red kangaroo?arrow_forward
- Physiology Doctors treated a patient at an emergency room from 2:00P.M.to7:00P.M.. The patient’s blood oxygen level L (in percent form) during this time period can be modeled by L=0.270t2+3.59t+83.1,2t7 where t represents the time of day, with t=2 corresponding to 2:00P.M.. Use the model to estimate the time (rounded to the nearest hour) when the patient’s blood oxygen level was 93.arrow_forwardComputer Virus The number V of computers infected by a virus increases according to the model Vt=100e4.6052t, where t is the time in hours. Find the number of computers infected after (a) 1 hour, (b) 1.5 hours, and (c) 2 hours.arrow_forward
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