Question

select the correct answer. as a result of changing sales figures, a company increased the size of its workforce very quickly at first and then more slowly, as shown in the table. which type of function best models the data? years after opening number of employees 1 100 2 348 3 405 4 575 5 654 6 704 7 746 a. a quadratic function with a positive value of a b. a quadratic function with a negative value of a c. a square root function d. a linear function with a positive slope

Explanation:

Step1: Analyze the growth pattern

The number of employees increases rapidly at first (from 100 to 348 in the first - second year) and then more slowly (from 704 to 746 from year 6 to year 7). A quadratic function \(y = ax^{2}+bx + c\) (\(a>0\)) has a non - linear growth pattern where the rate of change is not constant. A linear function has a constant rate of change. A square - root function \(y=\sqrt{x}\) has a decreasing rate of change as \(x\) increases which is not the case here.

Step2: Consider the form of quadratic function

A quadratic function \(y = ax^{2}+bx + c\) with \(a>0\) has an upward - opening parabola. The data shows an increasing trend which can be modeled by a quadratic function with a positive value of \(a\).

Answer:

A. a quadratic function with a positive value of a