SOLUTION: Hello. Referred to me by Minka. 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 correspond

Question 460029: Hello. Referred to me by Minka.
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?
b) the number of car accidents reached 21,600 in about what year?
(round to the nearest whole number, please).
Truly greatful to whom replies.
Samantha

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
A quadratic equation
-41x^2 + 1640x - 5856 = 0
Solve this using the quadratic formula:

in this equation; a=-41, b=1640, c=-5856

Two solutions but only this one will make sense

x =
x = +3.9 ~ 4 which is 2003, has about 21,600 accidents

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