Answer: 2019.08
Step-by-step explanation: To find the year when the car had the least value, we need to find the minimum value of the quadratic function V = 20x² - 363.2x + 2500, where x represents the number of years since 2010.
One way to find the minimum value is to use the formula for the vertex of a quadratic function, which is given by:
x = -b / (2a)
where a is the coefficient of the x² term, b is the coefficient of the x term, and x is the x-coordinate of the vertex.
In this case, a = 20 and b = -363.2, so we have:
x = -(-363.2) / (2 x 20)
x = 9.08
This means that the vertex of the parabola occurs at x = 9.08, which represents the year 2010 + 9.08 = 2019.08 (rounded to two decimal places).
Therefore, the car had the least value in the year 2019.