Question

The number of new cars purchased in a city can be modeled by the equation where C is the number of new cars and t is the number of years since 1958. C = 26t^2 + 168t + 4208. In what year will the number of new cars reach 15,000? a. 2026 b. 1993 c. 1970 d. 1976 Solve using the quadratic formula. HELP PLZ!

Answer 1

C(t)=26t^2+168t+4208, and we wish to know when C(t)=15000

26t^2+168t+4208=15000

26t^2+168t-10792=0

They want you to use the quadratic formula...

For a quadratic of the form ax^2+bx+c=0, the quadratic formula is:

x=(-b±√(b^2-4ac))/(2a), in this case we have:

x=(-168±√1122368)/52, since x>0

x≈17.14

1958+17.14≈1975.14

So by 1976 the number of new cars will reach 15000.