Chapter 4.5, Problem 14E

Reaction Time For certain decisions, the time it takes to respond is a logarithmic function of the number of choices faced. One model is,

$R=0.17+0.44\log N$

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.