select the correct answer.\nas a result of changing sales figures, a company increased the size of its…

select the correct answer.\nas 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.\n| years after opening | 1 | 2 | 3 | 4 | 5 | 6 | 7 |\n| number of employees | 100 | 348 | 405 | 575 | 654 | 704 | 746 |\nwhich type of function best models the data?\na. a quadratic function with a negative value of a\nb. a quadratic function with a positive value of a\nc. a square root function\nd. a linear function with a positive slope

select the correct answer.\nas 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.\n| years after opening | 1 | 2 | 3 | 4 | 5 | 6 | 7 |\n| number of employees | 100 | 348 | 405 | 575 | 654 | 704 | 746 |\nwhich type of function best models the data?\na. a quadratic function with a negative value of a\nb. a quadratic function with a positive value of a\nc. a square root function\nd. a linear function with a positive slope

Answer

Explanation:

Step1: Analyze quadratic functions

A quadratic function with a negative (a) value ((y = ax^{2}+bx + c,a<0)) is a parabola opening downwards, which would eventually start decreasing. Since the number of employees is increasing overall, option A is incorrect. A quadratic function with a positive (a) value ((y=ax^{2}+bx + c,a > 0)) is a parabola opening upwards. The rate of change of a quadratic function is not constant. The increase in the number of employees is initially large and then slows down, but not in the way a quadratic function with a positive (a) would behave (the rate of change of a positive - (a) quadratic function would increase after the vertex). So option B is incorrect.

Step2: Analyze square - root function

A square - root function (y = a\sqrt{x}+b) has a non - linear increasing behavior where the rate of change decreases as (x) increases. As (x) (years after opening) increases, the increase in (y) (number of employees) gets smaller, which is consistent with the data in the table where the company increased the size of its workforce very quickly at first and then more slowly.

Step3: Analyze linear function

A linear function (y=mx + b) with a positive slope (m) has a constant rate of change. But the data shows that the rate of increase in the number of employees is not constant (it starts large and then gets smaller), so option D is incorrect.

Answer:

C. a square root function