If the profit for producing x units can be approximated by the function P(x) = 0.002x³ + 100x, determine the marginal profit (profit per item), in dollars, for 50 units. $15 $5250 $250 $115

Element X is a radioactive isotope such that its mass decreases by 20% every year. Ifan experiment starts out with 730 grams of Element X, write a function to representthe mass of the sample after t years, where the monthly rate of change can be foundfrom a constant in the function. Round all coefficients in the function to four decimalplaces. Also, determine the percentage rate of change per month, to the nearesthundredth of a percent.

Describe what fixed costs and marginal costs mean to a company. Choose the correct answer below. A. Fixed cost is the rate of change of cost C(x) at the level of production x and is equal to the slope of the cost function at x. Marginal cost is the constant for a particular product and does not change as more items are made. O B. The number of units at which revenue just equals cost is the fixed cost. Marginal cost is the constant for a particular product and does not change as more items are made. O C. Fixed cost is the constant for a particular product and does not change as more items are made. Marginal cost is the rate of change of cost C(x) at the level of production x and is equal to the slope of the cost function at x. OD. Fixed cost is the constant for a particular product and does not change as more items are made. The number of units at which revenue just equals cost is the marginal cost.

Please write clearly

Suppose the revenue (in dollars) from the sale of x units of a product is given by 74x² + 81x 2x + 2 R(x) = Find the marginal revenue when 53 units are sold. (Round your answer to the nearest dollar.) $ Interpret your result. When 53 units are sold, the projected revenue from the sale of unit 54 would be $