The function f (t) = 310(1.025)" represents the change in a quantity over t weeks. What does the constant 1.025 reveal about the rate of change of the quantity? %3|

Q: The time rate of change of an alligator population P in a swamp is proportional to the square of P.…

A:

Q: Since the development of the iPod, the stock price of Apple has been growing rapidly and has been…

A: Given the development of the iPod that includes the stock price of Apple in which it grows rapidly…

Q: Snowballs formed by kids in winter season is found to melt in such a way that the rate of change in…

A:

Q: If a person's temperature after x hours of strenuous exercise is T(x) = x3(7 x2) + 98.6 degrees…

A:

Q: When the price of a certain commodity isp dollars per unit, customers demand x hundred units of the…

A: Given: x2+3px+p2=79 dpdt=-0.3$/month p=$5

Q: consider the equation f(x) = 2x2 - x find the average rate of change between x=3 and x=6

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Q: Find the average rate of change of g(x) 5æ – 5 from x = - 3 to a = 3.

A:

Q: A vehicle purchased for $32500 depreciates at a constant rate of 4%. Determine the approximate value…

A: Solving

Q: An oral medication is absorbed into the bloodstream at the rate of 4e-0.04 milligrams per minute,…

A:

Q: se the graph of the function to find its average rate of change from x= 1 to x = implify your answer…

A: Given query is to find average rate of change from the graph.

Q: Find the average rate of change of f(x) = 2x-7 from x = 3 to x = 6. Simplify your answer as much as…

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Q: Find the average rate of change of g(a) = 4x° + 3 from a = 2 to x = 2

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Q: Use this formula to find the instantaneous rate of change of the function at the given x-value.f(x)…

A: Given function is

Q: Find the average rate of change of f (x) = -x+5x+1 from x=2 to x=7. Simplify your answer as much as…

A:

Q: The Smiths bought an apartment for $75,000. Assuming that the value of the apartment will appreciate…

A: The Smiths bought an apartment for $75,000. Initial value of apartment is 75000  the apartment will…

Q: The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. a) What is the…

A: Applications of derivatives

Q: Find the average rate of change of g (x)=-2x- 3x from x=-2 to x=3. Simplify your answer as much as…

A: The given function is gx=-2x2-3x and the given points are x=-2 and x=3. When the value of x=-2, the…

Q: Given the g(x) function, what is the best estimate for the instantaneous rate of change at x=3? g(x)…

A:

Q: The concentration of a chemical agent in the bloodstream t hours after consumption is given by C(t)=…

A: Rate of change

Q: Find the average rate of change of g (x) = 3x-2x from x 3 to x 7. Simplify your answer as much as…

A:

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given: fx=x3,  x=5 inches

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 770…

A: Given: The cost function is given as, C(x)=770+38x-0.062x2 The objective is to find the rate at…

Q: If f(x) = 12x2 - x', what is the rate of change of f'(x) at (2, 40)? %3D Need Help? Watch It

A: Rate of change of f'(x)

Q: If y = 42x2 – 7x³ + x, what is the rate of change of y' at (1, 36)? Need Help? Read It

A: Rate of change of the function

Q: The function represents the rate of flow of money in dollars per year. Assume a 10-year period and…

A: Given that,  function f(x) = 0.03 x + 400 Rate r = 8 %  = 0.08 Time period is of 10 years. So time…

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 720…

A:

Q: The total cost of producing x shirts is: C(x) = 6000 + 30x, in dollars. Find the rate at which this…

A: Find the rate at which this average cost is changing when 10 shirts are being produced.

Q: Determine the instantaneous rate of change at x = 3 for g(x) = x² − 2x+5. A. 2 B. 4 C. 6 D. 8

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Q: Based on the graph above, estimate (to one decimal place) the average rate of change from x=1x=1 to…

A:

Q: For the function ?(?) = ?2 − 2? + 5, estimate for the instantaneous rate of change at x = 3. Round…

A:

Q: The total cost of producing x shirts is: C(x) = 6000 + 30x, %D in dollars. Find the rate at which…

A: Differentiate the cost function to calculate the rate of change of cost.

Q: Suppose that a person learns y items in x hours, as given by y = 20/x,0sxs9. Find the rate of…

A: Given y=20x       0≤x≤9The rate of learning in x hours is definedby derivative of y wrt…

Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units, (40 < x< 60) where x is the…

A:

Q: Find the average rate of change of f(x) = 3x2 - 2, from 2 to 4.

A:

Q: The length of a rectangle is increasing at a rate of 9 cm/s and Its width is increasing at a rate of…

A: Length of rectangle, x= 7 cm, Width of rectangle, y= 4 cm, Rate by which length is increasing is…

Q: The United States population (in millions) is predicted to be P(t) = 317e0.01t, where t is the…

A:

Q: The resale value R​ (in dollars) of a company car after t years is estimated to be given by…

A:

Q: Use the graph of the function to find its average rate of change from x=-4 to x=2. Simplify your…

A:

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

Q: What is the average rate of change of f(x) from x¡ = -2.6 to x2 = -1.3? Please write your answer…

A:

Q: Find the average rate of change of f (x) = 2x- 8x from x= 2 to x = 5. Simplify your answer as much…

A: We will find the average rate of change.

Q: If g(x) = 3x3 + 6x2 + 4. What is the value ofthe instantaneous rate of change of g(x) when x = -1?

A: We have to solve the problem

Q: Find the average rate of change of g(x)=−5x^3+5 from x=-3 to x=4

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Q: The rate of change of the income produced by a business selling face shields is given by f(t) =…

A:

Q: The graph shows the increase of cost of strawberries per pound in dollars, y, over a pesiod of…

A: we have to find the rate of increase of the cost of strawberries per pound through the linear graph…

Q: As y increases by 10,x Jncreases by 5. Which equation represents this rate of change? (7.1B, 7.1D,…

A: Rate of change = change in y /change in x

Q: estimate the instantaneous rate of change at the point indicated. P(x) = 3x^2 − 5; x = 2

A: To find the  the instantaneous rate of change at x=2 we need P'(2) We first find P'(x) using the…

Q: find the average rate of change of g(x)= -2x3 +5x2 from x=-1 to x=2 simplify your answer as much as…

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Q: what is the average rate of change of f(x)=log2(x) between 4 and 32. write the answer as a fraction

A: It is average rate of change.

Q: Find the percentage rate of change of f(x) at the indicated value of x. f(x) = 5500 – 2x²; x = 45

A:

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.