The area covered by a bacterial colony, in square centimeters, is modeled by the function A (t) = e for 0SIS 20 hours. At what time t is the instantaneous rate of change of the area equal to the average rate of change of the area over 0

Q: he marginal cost (rate of change of cost) in euros per unit of production for artilugios in a ertain…

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Q: hot air ballon is hovering 110 meters above the ground and begins to assend at a rate of 17 meters…

A: This is a question of application of differentiation and integration... We will proceed as follows

Q: The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on…

A: Average rate of change of f(x) on 3 ≤x ≤4 is f(4)-f(3)4-3

Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a) Find the rate of change…

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Q: The function y = f(x) is graphed below. What is the average rate of change of the function f (x) on…

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Q: the rate of change in thr profit (p) with respect to the number of units sold (x) is 0.0006x^2 +10.…

A: We can use the given equation to solve for profit

Q: A rectangle has width w inches and height h inches, where the width is twice the height. Both w and…

A: It is given that, a rectangle has width w inches and height h inches, where the width is twice the…

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

A: Solving

Q: With the given graph, estimate the instantaneous rate of change at x= -1 and show the steps. Next,…

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Q: Find the instantaneous rate of change Of the function at the Speciried value of X flx)=X?-2; X -3

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Q: amount

A: Please refer to the image below

Q: Find the total income produced by a continuous income stream in the first 10 years if the rate of…

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Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a)  Find the rate of…

A: Given:The radius r of a sphere is increasing at a rate of 6 inches per minute.

Q: The rate at which a radioactive chemical is delivered into cells is r(t) (measured in miligrams per…

A: NOTE: As method is not specified, question is solved for Riemann left end point approximation.

Q: The fungus Fusarium exosporium infects a field of flax plants through the roots and causes the…

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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.…

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Q: Q2/ An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

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Q: How do you solve?

A: Given, Side of square= x x(t)= 3t+1 Therefore, Area= (3t+1)*(3t+1) A(t)= 9t²+6t+1

Q: The rate (in mg carbon/m°/h) at which photosynthesis takes place for a species of phytoplankton is…

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Q: to determine the instantaneous rate of change c Use f(x+0.0001)-f(x) 0.0001 f(x) = 5x² - 7x ata = 2,…

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Q: Water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours after…

A: Given, water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours…

Q: A colony of fruit flies grows at a rate proportional to its size. At time t = 0, approximately 20…

A: Let the population of fruit flies be modelled by function y.  The question mentions that the rate is…

Q: The marginal profit obtained by selling x dollars of automobile insurance can be modelled by dP…

A: We will use the method of integration to calculate the change in profit.

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5/9x² –…

A:

Q: The growth in the population of a group of rabbits is given by P(t)= 800e0.08t, where P is the…

A: use derivative for finding the instantaneous rate

Q: The radius of a right circular cylinder is given by √(t + 2) and its height is 1/2√t, where t is…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: A balloon has just been inflated. Calculate the instantaneous rate of change by which the area…

A: Introduction: A geometric shape with a sphere-like appearance. In three dimensions, the sphere is…

Q: The edge of a cube decreases at a rate of 1.5m/s. Find the rate at which the surface area decreases…

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Q: A 2000-liter cistern is empty when waterbegins flowing into it (at t = 0) at a rate (in L/min) given…

A: It is given that   . Suppose a quantity Q changes over time at a known rate Q'. Then the net change…

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

Q: Let H(t) be the amount of raw honey at time t. During processing, the amount of raw honey present…

A: Answer is mentioned below

Q: ending from the surface. What is the best estimate of its instantaneous change in depth at t = 3 sec

A: In this question, the concept of the derivative is applied. Derivative A derivative is used to…

Q: A vehicle purchased for $29800 depreciates at a constant rate of 8%. Determine the approximate value…

A: cost price of vehicle=$29800 Constant rate of depreciates =8% per year We have to find the…

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: estimate the instantaneous rate of change at the point indicated.f (x) = ln x; x = 3

A: To find the instantaneous rate of change at x=3 we need f'(3) We find f'(x)

Q: estimate the instantaneous rate of change at the point indicated. f (x) = e^x ; x = 0

A: To find the instantaneous rate of change at x=0 we need f'(0) So we find f'(x)

Q: Estimate the instantaneous rate of change of the function f(x)=−x2+2x at x=−2 using the average rate…

A: We have been given a function f(x) = -x^2+2x and we need to find its instantaneous rate of change at…

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing…

A: topic - application of derivatives

Q: A cement mixer is pouring concrete in a conical pile. At the time when the height and base radius of…

A:

Q: The radius r of a sphere is increasing at a rate of 8 inches per minute. Find the rate of change of…

A:

Q: 6. Air is being pumped into a spherical ball at a rate of 7 cm³/sec. What is the rate of change of…

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Q: Find the average rate of change of h (x) = -2x+4x from x -2 to x 1. Simplify your answer as much as…

A:

Q: The radius of a right circular cylinder is given by   square root t + 9 and its height is 1/9…

A: GivenThe radius of a right circular cylinder and height is given by

Q: The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x2 + 10x + 5000. What is…

A:

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing…

A: We have to find area on Monday.

Q: Let H(t) be the amount of raw honey at time t. During processing, the amount of raw honey present…

A: We have to use exponential decay function to solve the problem

Q: Find the average rate of change of the function from x = 1 to x = 7. f(x) = 10x + x Additional…

A: Given that  f(x)=10x^2+x  x from 1 to 7  To find the average rate of change of function

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below