Chapter 1.3, Problem 16E

Reminder Round all answers to two decimal places unless otherwise indicated.

Wind Chill The graph in Figure $1.40$ shows the temperature T = T(v) adjusted for wind chill as a function of the velocity v of the wind when the thermometer reads $30$ degrees Fahrenheit. The adjusted temperature T shows the temperature that has an equivalent cooling power when there is no wind.

a. At what wind speed is the temperature adjusted for wind chill equal to $0$?

b. Your answer in part a is the solution of an equation involving T(v). Which equation?

c. At what value of v would a small increase in v have the greatest effect on T(v)? In other words, at what wind speed could you expect a small increase in wind speed to cause the greatest change in wind chill? Explain your reasoning.

d. Suppose the wind speed is 45 miles per hour. Judging from the shape of the graph, how significant would you expect the effect on T(v) to be if the wind speed increased?

FIGURE $1.40$ Temperature adjusted for wind chill when the thermometer reads $30$ degrees

Fahrenheit.