Hick's Law (namd for psychologist William Edmund Hicl says that when people must make a choice from a set options, the time it takes them increases logarithmica as the number of possible options increases. in particular, the law says that the time, T, it takes to make a choice can be modeled by the c guation

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 44E: Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program...
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Part 1 of 2
Hick's Law (namd for psychologist William Edmund Hick)
says that when people must make a choice from a set of
options, the time it takes them increases logarithmically
as the number of possible options increases.
In particular, the law says that the time, T, it takes to
make a choice can be modeled by the equation
T = b · log2 (n + 1)
where n represents the number of options from which to
choose, and b is a constant number (related to factors such
as the type of decision being made).
Suppose a software program has a drop-down menu with 8
different command options, and suppose it takes a user 5
seconds to make their choice from the drop-down menu.
What is the value of the constant b? Give your answer to
the nearest hundredth.
Answer: 1.58
Part 2 of 2
Using the value b = 1.58, suppose the software designers
decide that users should spend no more than 6 seconds to
make their choice on the drop-down menu. How many
choices can they put in the menu without going over the 6
second maximum?
Answer:
options
Transcribed Image Text:Part 1 of 2 Hick's Law (namd for psychologist William Edmund Hick) says that when people must make a choice from a set of options, the time it takes them increases logarithmically as the number of possible options increases. In particular, the law says that the time, T, it takes to make a choice can be modeled by the equation T = b · log2 (n + 1) where n represents the number of options from which to choose, and b is a constant number (related to factors such as the type of decision being made). Suppose a software program has a drop-down menu with 8 different command options, and suppose it takes a user 5 seconds to make their choice from the drop-down menu. What is the value of the constant b? Give your answer to the nearest hundredth. Answer: 1.58 Part 2 of 2 Using the value b = 1.58, suppose the software designers decide that users should spend no more than 6 seconds to make their choice on the drop-down menu. How many choices can they put in the menu without going over the 6 second maximum? Answer: options
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