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 2001.
B)Maximum revenue occurred during 1992.
C)Maximum revenue occurred during 2000.
D)Maximum revenue occurred during 2009.
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 2001. 
B)Maximum revenue occurred during 1992. 
C)Maximum revenue occurred during 2000. 
D)Maximum revenue occurred during 2009. 
E)Maximum revenue occurred during 1991.

Quizplus · Accepted Answer

The revenue function is given by R(t) = 11eb0d3b_97b5_618b_9790_57ebb98e83f3_TB1243_11 
We need to find the year in which maximum revenue occurs. 
To do so, we need to find the maximum value of the revenue function. 
Taking the derivative of the revenue function with respect to t, we get:
dR/dt = 11e^(0.1t)ln(11)e^(0.1t)
Setting this equal to zero to find the critical points:
11e^(0.1t)ln(11)e^(0.1t) = 0
e^(0.1t) = 0
There are no real solutions to this equation, which means that the maximum revenue occurs at an endpoint of the function. 
Plugging in t = 0 and t = 17 (since t is the number of years past 1992), we get:
R(0) = 11e^0 = 11
R(17) = 11e^(0.1*17) = 48.5
Therefore, the maximum revenue occurs in the year 2000 (which is 8 years past 1992). 
So the answer is C.

Assume That Sales Revenues for Continental Divide Mining Can Be