The rate of change of profit for a company is given by p(t) = 357 e-0.16t thousand dollars per year, t years since 2000, 0s ts 8. Check: p(2)=259.235206235308 p(t) thousand dollars per year t years since 2000 0 1 2 3 4 5 6 7 8 We wish to estimate the area trapped between p(t) and the t -axis fromt = 0 to t = 8 using two midpoint rectangles of equal width. (a) Complete the sigma notation for the area estimation described above by providing the width of each rectangle and the input values used to calculate the height of each rectangle. Area i = 1 where At = t2 = (b) Complete the calculation for the rectangle area estimation described above. Round your answer to 3 decimal places. Area = p(ti)At = i- 1 (c) What are the units for the area estimation described above? O thousand dollars per year O thousand dollars O vears

Q: The rate of change of profit for a company is given by p(t) = 357 e-0.18t thousand dollars per year,…

A: a) Given the function, p(t) = 357 e-0.18t  , 0 <=  t < = 8. That means a = 0, b = 8 and number…

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Q: Set up an integral for the length of the curve. 5) y = x6, 0 s x s 1 A) V1 + 6x5 dx B) + 6x10 dx 1…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.