Difficulty of a Task The difficulty in “acquiring a target” (such as using your mouse to click on an icon on your computer screen) depends on the distance to the target and the size of the target. According to Fitts’s Law, the index of difficulty (ID) is given by
where W is the width of the target and A is the distance to the center of the target. Compare the difficulty of clicking on an icon that is 5 mm wide to clicking on one that is 10 mm wide. In each case, assume that the mouse is 100 mm from the icon.
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Chapter 4 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
- Weight Gain Zoologists have studied the daily rate of gain in weight G as a function of daily milk energy intake M during the first month of life in several ungulate that is, hoofed mammal species. Both M and G are measured per unit of mean body weight. They developed the model G=0.067+0.052logM With appropriate units for M and G. a.Draw a graph of G versus M. Include values of M up to 0.4unit. b.If the daily milk-energy intake M is 0.3unit, what is the daily rate of gain in weight? c.A zookeeper wants to bottle-feed an elk calf so as to maintain a daily rate of gain in weight G of 0.3unit. What must the daily milk-energy intake be? d.The study cited above noted that the higher levels of milk ingested per unit of body weight are used with reduced efficiency. Explain how the shape of the graph supports this statement.arrow_forwardLogarithmic Equations Use the definition of the logarithmic function to find x. (a) Inx=3 (b) Ine2=xarrow_forwardLogistic Population growth the table and scatter plot give the population of black flies in a closed laboratory container over an 18 day period. (a) Use the logistic command on your calculator to find a logistic model for these data. (b) Use the model to estimate the time when there were 400 flies in the containerarrow_forward
- Reaction Time For certain decisions, the time it takes to respond is a logarithmic function of the number of choices faced. One model is, R=0.17+0.44logN where R is the reaction time in seconds and N is the number of choices. a.Draw a graph of R versus N. Include values of N from 1 to 10 choices. b.Using functional notation, express the reaction if there are seven choices, and then calculate that time. c.If the reaction is to be at most 0.5 second, how many choices can there be? d.If the number of choices increases by a factor of 10, what happens to the reaction time. e.Explain in practical terms what the concavity of graph means.arrow_forwardWealth Distribution Vilfredo Pareto (18481923) observed that most of the wealth of a country is owned by a few members of the population. Paretos Principle is logP=logcklogW where W is the wealth level how much money a person has and P is the number of people in the population having that much money. aSolve that equation for P. bAssume that k=2.1 and c=8000, and that W is measured in millions of dollars. Use part a to find the number of people who have 2 million or more. How many people have 10 million or more?arrow_forwardWealth Distribution Vilfredo Pareto (1848-1923) observed that most of the wealth of a country is owned by a few members of the population. Pareto's Principle is logP=logcklogW where W is wealth level (how much a has) and P is the number of people in the population having that much (a) Solve the equation for P. (b) Assume that k 2. I and c and that W is measured in millions Of dollars. Use (a) to find the number of people who have $2 million or more. How many people have SIO million or more?arrow_forward
- Logarithmic and Exponential Forms Complete the table by finding the appropriate logarithmic or exponential from of the equation, as in Example 1.arrow_forwardStride Frequency of Animals Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal. Use the table to find a logarithmic equation that relates an animal’s weight x (in pounds) and its lowest stride frequency while galloping y (in strides per minute).arrow_forwardExpanding Logarithmic Expressions Use the laws of Logarithms to expand the expressions. Ina3arrow_forward
- Human Memory Model Students in a mathematics class took an exam and then took a retest monthly with an equivalent exam. The average scores for the class are given by the human memory model ft=8017logt+1,0t12 where t is the time in months. (a) Use a graphing utility to graph the model over the specified domain. (b) What was the average score on the original exam t=0 ? (c) What was the average score after 4 months ? (d) What was the average score after 10 months ?arrow_forwardDomain Find the domain of the function. g(x)=log3(x21)arrow_forward
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