according to data from the national safety council, the fatal-accident rate per 100,000 licensed drivers can be approximated by the function
f(x)=.0328x^2 - 3.55x + 115, where x is the age of the driver (16< or equal to x < or equal to 88). at what age is the rate the lowest?
To find the age at which the rate is the lowest, we need to minimize the given function f(x) = 0.0328x^2 - 3.55x + 115.
There are a few different methods to find the minimum of a quadratic function, such as completing the square or using the quadratic formula. Since the given function is in the form of a quadratic equation, we can use the formula for finding the x-coordinate of the vertex.
The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b / (2a). In our case, a = 0.0328 and b = -3.55.
Using the formula x = -b / (2a), we can substitute the values of a and b into the equation:
x = -(-3.55) / (2 * 0.0328)
x = 3.55 / 0.0656
x ≈ 54.02
Therefore, the age at which the rate is the lowest is approximately 54.