Question 1207526
{{{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?

 {{{t =0}}}

{{{S(0) = 4 + 31* ln(0+1)=4}}}

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

{{{t=3}}} months

{{{S(3) = 4 + 31* ln(3+1)=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( 600, 600, -10, 10, -10, 55, 4 + 31*ln(x + 1), 50) }}}


{{{50 = 4 + 31*ln(t + 1)}}}

{{{31*ln(t + 1)=50-4}}}

{{{ln(t + 1)=46/31}}}

{{{t + 1=e^(46/31)}}}

{{{t = e^(46/31) - 1}}}

{{{t=3.4099835872593687}}}

{{{t=3}}}months and {{{12.5}}} days
     

{{{ drawing( 600, 600, -10, 10, -10, 55,
blue(line(3.4,50, 3.4,0)),
graph( 600, 600, -10, 10, -10, 55, 4 + 31*ln(x + 1), 50)) }}}