To study how recognition memory decreases with time, the following experiment was conducted. The subject read a list of 20 words slowly aloud, and later, at different time intervals, was shown a list of 40 words containing the 20 words that he or she had read. The percentage, $P$, of words recognized was recorded as a function of $t$, the time elapsed in minutes. The table below shows the averages for 5 different subjects. This is modeled by $P=a\ln t +b$.

(a) Find $\ln{t}$ for each value of $t$ in the table above, and then use linear regression on a calculator to estimate $a$ and $b$ in the linear fit $P= a \ln{t} +b$. In the blanks below, enter the corresponding values for $a$ and $b$:
$a =$
$b =$
(round values to 4 decimal places)

(b) When does this model (in part a) predict that the subjects will recognize no words?
In DAYS (1440 minutes = 1 day)

(c) When does this model (in part a) predict that the subjects will recognize all words?
In SECONDS.