Question

The number of new cars purchased in a city can be modeled by the equation C = 20t^2 + 135t + 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 new cars purchased reach 15,000?

a) 2002
b) 2004
c) 2006
d) 2008

Answer 1

To find the year when the number of new cars purchased will reach 15,000, substitute C = 15000 into the equation C = 20t^2 + 135t + 3050, rearrange to form a quadratic equation, use the quadratic formula to solve for t, and add 1998 to find the year.

Step-by-step explanation:

To find the year when the number of new cars purchased will reach 15,000, we need to solve the equation C = 20t^2 + 135t + 3050 for t. Here's how:

1. Substitute C = 15000 into the equation: 15000 = 20t^2 + 135t + 3050
2. Rearrange the equation to form a quadratic equation: 20t^2 + 135t - 11950 = 0
3. Use the quadratic formula to solve for t: t = (-b ± √(b^2 - 4ac)) / 2a
4. Calculate the value of t using the quadratic formula: t ≈ -10.45 or t ≈ 5.45
5. Since t represents the number of years since 1998, we need to add 1998 to find the year: 1998 + 5.45 ≈ 2004 or 1998 - 10.45 ≈ 1988

Therefore, the number of new cars purchased will reach 15,000 in approximately the year 2004.