Question 1153501


Abercrombie and Fitch stock had a price given as 

{{{P = 0.2t^2 -5.6t + 50.2}}}

 where {{{t}}} is the time in months from 1999 to 2001. ({{{t = 1}}} is January 1999). 

Use MS-Excel to find the two months in which the price of the stock was ${{{31}}} or ${{{30}}}.

{{{P = 0.2t^2 -5.6t + 50.2}}} if ${{{P=31}}}

{{{31= 0.2t^2 -5.6t + 50.2}}}

{{{ 0.2t^2 -5.6t + 50.2-31=0}}}

{{{ 0.2t^2 -5.6t + 19.2=0}}}...factor

{{{ 0.2(t^2 -28t + 96)=0}}}

{{{ 0.2(t^2 -24t-4t + 96)=0}}}

{{{ 0.2((t^2 -24t)-(4t - 96))=0}}}

{{{ 0.2(t(t -24)-4(t - 24))=0}}}

{{{0.2 (t - 24) (t - 4) = 0}}}

solutions: 

if {{{(t - 24)  = 0}}}->{{{t=24}}}
if {{{ (t - 4) = 0}}}->{{{t=4}}}

 the two months in which the price of the stock was ${{{31}}}, {{{t = 1}}} is January 1999: 

{{{t = 4}}} is April 1999
{{{t = 24}}} is January 2001


{{{P = 0.2t^2 -5.6t + 50.2}}} if ${{{P=30}}}

{{{30= 0.2t^2 -5.6t + 50.2}}}

{{{ 0.2t^2 -5.6t + 50.2-30=0}}}

{{{ 0.2t^2 -5.6t + 20.2=0}}}...use quadratic formula

{{{ t=(-b+-sqrt(b^2-4ac))/2a}}}......{{{a=0.2}}},{{{b=-5.6}}},{{{c=20.2}}}

{{{ t=(-(-5.6)+-sqrt((-5.6)^2-4*0.2*20.2))/(2*0.2)}}}

{{{ t=(5.6+-sqrt(31.36-16.16))/0.4}}}

{{{ t=(5.6+-sqrt(15.2))/0.4}}}

{{{ t=(5.6+-3.9)/0.4}}}

solutions: 

{{{ t=(5.6+3.9)/0.4}}}=>{{{ t=23.75}}}-> not full month

{{{ t=(5.6-3.9)/0.4}}}=>{{{ t=4.25}}}-> not full month

the two months in which the price of the stock was ${{{30}}}: none