Question

fa25 math 125 - 09: precalculus i homework: ch 1.2 operations with algebraic expressions question 18, 1.2.49 - be hw score: 94.44%, 17 of 18 points o points: 0 of 1 the costs (in millions of dollars) for a certain company can be approximated by the polynomial 10.2x^{3}-431.7x^{2}+6581x - 27,518, where x = 7 corresponds to the year 2007. determine whether the following statement is true or false. the costs were higher than $7500 million in 2014. since the costs (in millions of dollars) for 2014 were $□ million, the statement is □ (round to the nearest whole number as needed.)

Explanation:

Step1: Determine the value of x for 2014

Since x = 7 corresponds to 2007, for 2014, x=7+(2014 - 2007)=14.

Step2: Substitute x = 14 into the polynomial

Let \(C(x)=10.2x^{3}-431.7x^{2}+6581x - 27518\).
Substitute x = 14:

$$
LATEXBLOCK0
$$

Step3: Round the result and check the statement

Rounding 7991.6 to the nearest whole - number gives 7992. Since 7992>7500, the statement is true.

Answer:

7992, true