The cost of mining a ton of coal is rising faster every year. Suppose is the cost of mining a ton of coal at time t. Which of the following must be increasing? Select all that apply.

Question

The cost of mining a ton of coal is rising faster every year. Suppose  is the cost of mining a ton of coal at time t. Which of the following must be increasing? Select all that apply.

Quizplus · Accepted Answer

The cost of mining a ton of coal is represented by 11eb69ff_fe85_55e8_af94_f70d4abc0175_TB8190_11. To determine whether it is increasing, we need to look at the coefficients of the terms. As time t increases, if the coefficients of the terms with higher powers of t are positive, then the cost is increasing.

A) 11eb69ff_fe85_55e9_af94_0912bb573e81_TB8190_11: This choice differs from the original term by changing the coefficient of the t term. As long as the coefficient is positive, it is increasing.

B) 11eb69ff_fe85_7cfa_af94_a9667b38e85b_TB8190_11: This choice differs from the original term by changing the coefficient of the t^2 term. Since t^2 is a higher power of t than t, a positive coefficient indicates that the cost is increasing faster than linearly.

C) 11eb69ff_fe85_7cfb_af94_6736bd4786cd_TB8190_11: This choice differs from the original term by changing the coefficient of the constant term. The constant term does not depend on t, so changing its coefficient does not affect whether the cost is increasing or decreasing.

The Cost of Mining a Ton of Coal Is Rising