Explore the solutions to various mathematics and economics problems, covering topics such as curve analysis, profit maximization, and matrix operations. Delve into the world of mathematical modeling and economic analysis.
Extract
[...] We therefore have . b . We deduce that is a geometric sequence of ratio . The first term is . So we can write for all . As on a alors . d July 2024 corresponds to so colonies To find out how many years are needed to double the number of colonies, we need to replace the condition 'While C [...]
[...] is represented by the curve car - (slope of the tangent at the origin is - on so is increasing on this interval - on so is decreasing on this interval is represented by the curve car - sur so is increasing on this interval - on so is decreasing on this interval The representative curve of admits a point of inflection where its second derivative is zero, that is, at the point of coordinates . Exercise 4 b The coefficients of the matrix represent the cost per model. Yes are the new hourly costs so we can write the following matrix product: . By developing the matrix product we get well: The matrix is invertible and we have The previous system is written as with and . So . Exercise 5 We have , so there exists a matrix such as . is therefore reversible . [...]
[...] Exercise 2 Part A so no solution So we have , so . The function is therefore strictly increasing on and a fortiori on . et a concave convex The curve admits a point of inflection at the point of coordinates . Part B The recipe function is given by the line of equation : a To achieve a positive profit, the revenue curve must be above the cost curve, which is the case for b Graphically, the production for which the profit is maximized corresponds to . [...]
