Chapter 1.8, Problem 33E

Technology exercises

Judgment Time In a psychology experiment, people improved their ability to recognize common verbal and semantic information with practice. Their judgment time after $t$ days of practice was $f\left(t\right)=.36+.77{(t-.5)}^{-0.36}$ seconds. (Source: American Journal of Psychology.)

(a) Display the graphs of $f\left(t\right)$ and $f\text{'}\left(t\right)$ in the window $\left[.5,6\right]$ by $\left[-3,3\right]$. Use these graphs to answer the following questions.

(b) What was the judgment time after $4$ days of practice?

(c) After how many days of practice was the judgment time about $.8$ second?

(d) After 4 day of practice, at what rate was judgment time changing with respect to days of practice?

(e) After how many days was judgment time changing at the rate of $-.08$ second per day of practice?