Question

The table shows the relationship between the length, in inches, of a rectangular package and the cost to mail it.
length 1 2 3 4 5
cost 3.50 8.50 23.50 54.50 107.50


The equation C(l) = l3 – l2 + l + 2.5 models the cost to mail a package as a function of its length. To the nearest quarter inch, approximately what is the length of a package that costs $11.00 to mail? Enter your answer as a decimal.

inches

Answer 1

Solve C(l) = 11:
l^3 − l^2 + l + 2.5 = 11 → l^3 − l^2 + l − 8.5 = 0.

Numerically the solution is about l ≈ 2.243 inches. Rounded to the nearest quarter inch (0.25 in) gives 2.25 inches.

Answer: 2.25 inches