SOLUTION: The following function models the average typing speed S, in words per minute, of a student who has been typing for t months. S(t) = 4 + 31 ln(t + 1), 0 ≤ t ≤ 16 (a) What

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The following function models the average typing speed S, in words per minute, of a student who has been typing for t months. S(t) = 4 + 31 ln(t + 1), 0 ≤ t ≤ 16 (a) What       Log On


   

Question 1207526: The following function models the average typing speed S, in words per minute, of a student who has been typing for t months.
S(t) = 4 + 31 ln(t + 1), 0 ≤ t ≤ 16
(a) What was the student's average typing speed, to the nearest word per minute, when the student first started to type?
What was the student's average typing speed, to the nearest word per minute, after 3 months?


(b) Use a graph of S to determine how long, to the nearest tenth of a month, it will take the student to achieve an average typing speed of 50 words per minute.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
S%28t%29+=+4+%2B+31%2Aln%28t+%2B+1%29, 0+%3C=+t+%3C=+16
(a) What was the student's average typing speed, to the nearest word per minute, when the student first started to type?
t+=0
S%280%29+=+4+%2B+31%2A+ln%280%2B1%29=4
What was the student's average typing speed, to the nearest word per minute, after 3 months?
t=3 months
S%283%29+=+4+%2B+31%2A+ln%283%2B1%29=46.97512519471661=47

(b) Use a graph of S to determine how long, to the nearest tenth of a month, it will take the student to achieve an average typing speed of 50 words per minute.


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+55%2C+4+%2B+31%2Aln%28x+%2B+1%29%2C+50%29+

50+=+4+%2B+31%2Aln%28t+%2B+1%29
31%2Aln%28t+%2B+1%29=50-4
ln%28t+%2B+1%29=46%2F31
t+%2B+1=e%5E%2846%2F31%29
t+=+e%5E%2846%2F31%29+-+1
t=3.4099835872593687
t=3months and 12.5 days