Question

The number of new cars purchased in a city can be modeled by the equation C=20t to the 2nd power, where C is the number of new cars and t = 0 corresponds to the number of new cars purchased in 1998. In what yr. will the number of new cars purchased reach 15,000?​

Answer 1

`1998 + 5√(30)`

Explanation:

Set up the equation:

Since C(t) gives the number of cars purchased in the t-th year after 1998, then make the number of cars equal to 15 000 and solve for t - the year:

20t^2 = 15000

t^2 = 750

t =
`√(750) = √(10) \cdot √(25) \cdot √(3) = 5√(30)`

The year will be simply 1998 + 5 \sqrt{30}