Question

The number of new cars purchased in a city can be modeled by the equation = 20t² + 135+ + 3050, where C is the number of new cars and t = 0 corresponds to the number of new cars purchased in 1998. In what year will the number of ew cars purchased reach 15,000?

a) 2001
b) 2002
c) 2003
d) 2004

Answer 1

To find the year when the number of new cars purchased reaches 15,000, solve the given equation by factoring or using the quadratic formula. The values of t are approximately -6.77 and 6.77, which correspond to the years 1998 and 2005, respectively.

Step-by-step explanation:

To find the year when the number of new cars purchased reaches 15,000, we need to solve the equation 20t² + 135t + 3050 = 15,000.

First, subtract 15,000 from both sides to get 20t² + 135t + 3050 - 15000 = 0.

Next, simplify and solve the quadratic equation. In this case, we can use factoring or the quadratic formula to find the values of t. Once we find the values of t, we can determine the corresponding years.

In this case, the values of t will be approximately -6.77 and 6.77. Since t = 0 corresponds to the number of new cars purchased in 1998, we need to find the corresponding years for t = -6.77 and t = 6.77. Adding 6.77 to 1998 gives us the year approximately 2005, which is when the number of new cars purchased will reach 15,000.