The following function models the average typing speed S, in words per minute, of a student who has been typing for t months

Question

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 4ln(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?

 ____ words/min

What was the student's average typing speed, to the nearest word per minute, after 3 months?

_______ words/min

(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 65 words per minute.

_____ months

Answer 1

First of all , the function can be

slightly simplified:

S(t) = 4 + 31 * 4 ln(t+1)

= 4 + 124*ln(t+1)

part A:

Beginning typist --> t =0

S(0) = 4 + 124 ln(0+1)

= 4 + 124 ln 1

= 4 + 124*0

= 4 + 0

= 4

part B:

t=3 months

S(3) = 4 + 124*ln(3+1)

= 4 + 124*ln 4

= 176

part c:

65 = 4 + 124*ln (t+1)

61 = 124 ln(t+1)

61/124 = ln(t+1)

exp(61/124) = t+1

exp(61/124)-1 = t

1.63... - 1 = t

0.63... months

about 2+1/2 weeks