Since YouTube first became available to the public in mid-2005, the rate at which video has been uploaded to the site can be approximated by v(t) = 1.1t2 - 2.6t + 2.3 million hours of video per year (0

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Given that ,    Ecologist estimate that, when the population of a certain city is x thousand…

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A: It is given that at t=0 bacteria population is 7000   The growth rate is 1000*4t

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A: (b)

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A:

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A: We need to find rate of change.

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A: Let's find rate of area increasing when W=4cm and l=10cm.

Q: From the beginning of the year 2000, the annual world demand for oil has increased. To account for…

A: Let's find.

Q: From the beginning of the year 2000, the annual world demand for oil has increased. To account for…

A: Topic:- exponential growth function

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Q: #2. Researchers have descried the maximum growth rate of a phytoplankton as a function of the cell…

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Q: A species of rabbits has a growth rate of 0.625 a month. If a population of foxes inhabits the same…

A: Given Growth rate of rabbits = 0.625 a month Foxes kills 10 rabbit per day

Q: 2. Consider a population of bacteria that grows according to the function f(t)=500e^0.05t , where t…

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A: Given that, After an antibiotic tablet is taken, the concentration of the antibiotic in the…

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Q: #3 Find the instantaneous rate of change for the function f(x) = V3 – x at x = -6.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: A manufacturer estimates that she can sell a maximum of 105 thousand cell phones in a city. By…

A: image is attached

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Q: The number of bacteria in a culture is given by the function n(t)=950e^0.35t where t is measured…

A: The number of bacteria in a culture is given by n(t) = 950e^{0.45t}e0.45t

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Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x…

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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.