Final answer:
The question asks for the age with the least accidents according to the quadratic function. The age that minimizes the function can be found by calculating the vertex of the parabola, which leads to the answer being the age group of 50 years.
Step-by-step explanation:
The student's question revolves around finding the age that has the least number of accidents according to a quadratic function f(x)=0.013x²−1.35x+48, within the age range of 16 to 85 years. To solve this, we look for the age x that minimizes the function, which can be found by calculating the vertex of the parabola. Because the coefficient of x² is positive, the parabola opens upwards, and the vertex will give us the minimum value.
The x-coordinate of the vertex of a parabola given by f(x) = ax² + bx + c is found using the formula x = -b/(2a). Here, a = 0.013 and b = -1.35. Plugging these into the formula gives us x = -(-1.35)/(2 × 0.013) = 51.9231, which we round to the nearest whole number, 52. Looking at the options provided:
The age closest to 52 is 50. Therefore, the correct answer is c) 50, which is the age group that has the least number of accidents according to the given function.