Assume that sales revenues for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs.
A) Maximum revenue occurred during 1998.
B) Maximum revenue occurred during 1992.
C) Maximum revenue occurred during 1997.
D) Maximum revenue occurred during 2003.
E) Maximum revenue occurred during 1991.

Question

Assume that sales revenues for Continental Divide Mining can be described by  , where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs. ​
A) Maximum revenue occurred during 1998. 
B) Maximum revenue occurred during 1992. 
C) Maximum revenue occurred during 1997. 
D) Maximum revenue occurred during 2003. 
E) Maximum revenue occurred during 1991.

Quizplus · Accepted Answer

The given function is 11ea984b_af59_f9a9_9029_491d595649d5_TB4005_11, which means that the revenue is a quadratic function of time with a negative coefficient of the squared term. Therefore, the graph of the function is a downward facing parabola with a maximum point. To find the year in which maximum revenue occurs, we need to find the vertex of the parabola. The vertex of the parabola is given by the formula t = -b/2a, where a and b are the coefficients of the squared and linear terms in the function, respectively.

In this case, a = -11,000 and b = 10,450. Therefore, t = -(10,450)/(2*(-11,000)) = 0.475.

Since t represents the number of years past 1992, we need to add 0.475 to 1992 to get the year in which maximum revenue occurs.

1992 + 0.475 = 1992.475

Therefore, maximum revenue occurs in the year 1997.

The correct answer is C.

Assume That Sales Revenues for Continental Divide Mining Can Be