Profit Function Modeling
The profit P(x), in thousands of dollars, for a company is a function of the number of units x produced. The function satisfies the following conditions: P(0) = -50, representing fixed costs; P(100) = 150; and as x becomes very large, the rate of change of profit approaches 2. Which of the following functions best models this situation?
A
P(x) = 2x - 50(1 - e^{-0.01x})
B
P(x) = -50 + 2x - 100(1-x/100)
C
P(x) = 2x - 50
D
P(x) = 2x - 50 - 100e^{-0.01x}
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