```Question 460029
The cumulative number of car accidents from 2000 to 2010 can be modeled by the quadratic expression,
C= -41x^2+1640x+15,744, where x=1 corresponds to 2000, x=2 corresponds to 2001, and so on until x=11 corresponds to 2010.
:
a) find the number of cumulative car accidents in 2005?
for 2005, x=6
C = -41(6^2) + 1640(6) + 15744
C = -41(36) + 9840 + 15744
C = -1436 + 9840 + 15744
C = 24,108 accidents in 2005
:
b) the number of car accidents reached 21,600 in about what year?
(round to the nearest whole number, please).
C = 21600, write the equation
-41x^2 + 1640x + 15744 = 21600
-41x^2 + 1640x + 15744 - 21600 = 0
-41x^2 + 1640x - 5856 = 0
Solve this using the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in this equation; a=-41, b=1640, c=-5856
{{{x = (-1640 +- sqrt(-1640^2-4*-41*-5856 ))/(2*-41) }}}
:
{{{x = (-1640 +- sqrt(2689600-960384 ))/(-82) }}}
:
{{{x = (-1640 +- sqrt(1729216 ))/(-82) }}}
Two solutions but only this one will make sense
{{{x = (-1640 + 1315)/(-82) }}}
x = {{{(-325)/(-82)}}}
x = +3.9 ~ 4 which is 2003, has about 21,600 accidents
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