Question

A construction crew is paving a road. The crew has already paved 1,000 square feet and can pave at a rate of 300 square feet of road per hour. The function f(x) = 300x + 1,000 represents this situation.

What is f(3), and what does it represent?

A. 900 square feet; f(3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
B. 900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.
C. 1,900 square feet; f(3) represents the number of additional square feet the construction crew has paved after 3 hours, not including the initial paved amount.
D. 1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.

Answer 1

The function of the construction crew is an illustration of a linear function

The value of f(3) is 1900, and f(3) represents the total number of square feet paved after working for 3 hours

The function is given as:

$\mathbf{f(x) = 300x + 1000}$

To calculate f(3), we substitute 3 for x

$\mathbf{f(3) = 300 \times 3 + 1000}$

Multiply 300 and 3

$\mathbf{f(3) = 900 + 1000}$

Add 900 and 1000

$\mathbf{f(3) = 1900}$

This means that the value of f(3) is 1900.

And it represents the total number of square feet paved after working for 3 hours

Hence, the correct option is (D)

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