SOLUTION: The number of new cars purchased in a city can be modeled by the equation C =18t^2 + 174t + 6241, where C is the number of new cars and t = 0 corresponds to the number of new cars
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Question 192217: The number of new cars purchased in a city can be modeled by the equation C =18t^2 + 174t + 6241, where C is the number of new cars and t = 0 corresponds to the number of new cars purchased in 1972. In what year will the number of new cars reach 35,000? I have tried using the quadratic equation, but I get a strange answer.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I presume you performed the calculation thusly:
 = 18t^2 + 174t + 6241)
Where
 = 35000)
So:
Using the quadratic formula:
(-28579)}}{2(18)} )
Which, after a bit of prime factoring work and calculator button punching becomes:
Now, reading the problem carefully,  = 6241)
is the number of new cars sold in 1972. That means that 6241 new cars were sold by the end of 1972. So, 35 years later, you would be at the end of 1972 plus 35 = 2007, and at that time you would not have quite reached the 35,000 number.  = 18(35)^2 + 174(35) + 6241 = 34381)
. So you trip the 35,000 number right around 3:22 AM June 5, 2008, roughly speaking.
John
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