Final answer:
The question calculates the total cost of producing 400 units using a given cost function. There was a miscalculation in the provided steps, and the correct total cost, after accurate computation, should be approximately $3,371.15.
Step-by-step explanation:
The question involves using a cost function, which is a mathematical expression that estimates the total cost of producing a given number of units in a company. This typically falls under the subject of Mathematics, specifically within the topic of functions and their applications in real-world scenarios such as economics and business. The question requires the student to find the total cost of producing 400 units using the provided cost function c(x) = 875 ln(x + 10) - 1900. By substituting x with 400 and calculating the cost, the student arrives at the total production cost.
Example Calculation:
c(400) = 875 ln(410) - 1900
Using a calculator to compute the natural logarithm, ln(410) approximately equals 6.0189. Thus,
c(400) = 875 * 6.0189 - 1900
Multiplying and subtracting, we get approximately $5271.15 - $1900, which is about $3371.15, not $7171.15 as stated in the question. It seems there is a miscalculation in the initial statement. Correctly rounded to the nearest cent, the total cost is approximately $3371.15.