Answer:
f(x) = 4x² + 100x + 600 represents the function of the area.
Explanation:
We are given that the area of the land is f(x) where x is the width of the uniform border, in miles.
Now, from the functions in the options given, let's try f(1) & f(2)for each of them;
f(1) for 150x³ + 554 is;
150(1³) + 554 = 150 + 554 = 704
For f(2);
150(2³) + 554 = 1200 + 554 = 1754
f(1) = 704 tallies with the given value of 704 but f(2) = 1754 does not tally with the given value of 816, thus, 150x³ + 554 does not represent the function of the area
For f(1) into 100x³ + 250x + 354, it gives;
f(1) = 100(1³) + 250(1) + 354
f(1) = 100 + 250 + 354
f(1) = 350 + 354
f(1) = 704
For f(2);
f(2) = 100(2³) + 250(2) + 354
f(2) = 800 + 500 + 354
f(2) = 1654
f(1) = 704 tallies with the given value of 704 but f(2) = 1654 does not tally with the given value of 816, thus, 100x³ + 250x + 354 does not represent the function of the area.
For f(1) into 4x² + 700:
f(1) = 4(1²) + 700
f(1) = 4 + 700
f(1) = 704
f(2) = 4(2²) + 700
f(2) = 16 + 700
f(2) = 716
f(1) = 704 tallies with the given value of 704 but f(2) = 716 does not tally with the given value of 816, thus, 4x² + 700 does not represent the function of the area.
For f(x) = 4x² + 100x + 600:
f(1) = 4(1²) + 100(1) + 600
f(1) = 4 + 100 + 600
f(1) = 704
f(2) = 4(2²) + 100(2) + 600
f(2) = 16 + 800
f(2) = 816
f(1) = 704 tallies with the given value of 704 and f(2) = 816 also tallies with the given value of 816, thus, 4x² + 100x + 600 represents the function of the area.