Water flows into and out of a storage tank. A graph of the rate of change r(t)of the volume of water in the tank, in liters per day, is shown. If the amount of water in the tank at time t =0 is 25,000 L, use the Midpoint Rule to estimate the amount of water four days later.

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: Because of the absence of predators, the number of rabbits on a small island increases at a rate of…

A: Given that the growth function is: y(t) = y0ekt. At, t=0, y(0) = y0 [This is the initial…

Q: For the function y = x2 , find the instantaneous rate ofchange of y with respect to x when x = 3.

A: The instantaneous rate of change of y with respect to x is given by dy/dx

Q: When polluted water begins to flow into an unpolluted pond, the concentration of pollutant, c, in…

A:

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

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Q: amount

A: Please refer to the image below

Q: For the function y=x2,compute the average rate of change between x=9 and x=10

A: We have to find the average rate of change of function.

Q: Consider the function f (x) = x2. Calculate the rate of change of f (x) at x = 1, and compare your…

A: Consider the function f (x) = x2  To Calculate the rate of change of f (x) at x = 1.

Q: Find the rate of change of total profit, in dollars, with respect to time where R(x) = 4x and dx…

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Q: 4. The path of a baseball relative to the ground can be modelled by the function dlt) = – f² + 8t +…

A: derivative

Q: Find the rate of change of total profit, in dollars, with respect to time where R(x) = 90x – 0.5æ2…

A: A detailed solution is given below

Q: If a ball is thrown into the air with a velocity of 40 fts, its height in feet seconds later is…

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Q: In the equation, x² +y² = 45, what is the value of the rate of change in y with respect to time t…

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Q: In a simple physical apparatus, the distance x cm and y cm are connected by the relation 1.1 1…

A: Distance x cm and y cm are connected by the relation 1x+1y=19 ....(1) x is increasing at the rate of…

Q: For a certain animal, the surface area S of the body is related to the body's weight W according toS…

A: The surface area S of the body is related to the body's weight W according to S is:

Q: 3. fox =V X at X T6

A:

Q: the number of cell phone subscribers in a certain country in the early 2000s was projected to follow…

A: We use differentiation and integrations to solve this problem.

Q: Find the instantaneous rate of change for the function at the given value. g(t) = 4 – t² at t = - 6

A: Consider the function fx=x2+4x We have to find the instantaneous rate of change for the function…

Q: The number of bacteria in a culture is given by the function n(t)=960e0.4tn(t)=960e0.4t where tt is…

A: To find- relative rate of growth of this bacterium population

Q: In the equation, x² + y² = 45, what is the value of the rate of change in y with respect to time t…

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Q: Estimate the instantaneous rate of change given the following: f(x) =5 at the point (-3, — 2/1) x+5…

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

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Q: Find x0 given that the rate of change of y =2x2+x-1 with respect to x at x=x0 is 4

A: giveny =2x2+x-1 rate of change=4rate of change=dydxdydx=4x+1

Q: from the edge of a cliff into described by the function ht rate of change in the height - 4.9t² +…

A: Formula average height change=(h(b)-h(a))/(b-a) Where a=4second b=5second

Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

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

A: Given that the monthly output at the Olek Carpet Mill is

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: Because of heavy rainfall, the water level in a reservoir is rising at a rate of g(t) feet per hour,…

A: Given problem :- Because of heavy rainfall, the water level in a reservoir is rising at a rate of…

Q: For the function y = x3, compute the average rate ofchange between x = -1 and x = 2.

A: We have given function y=x3

Q: Suppose that the spread of a disease through the student body at an isolated college campus can be…

A: Here we have to find out rate of change of y.

Q: If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does (see picture)…

A: solution is given below

Q: If the rate of change in life expectancy I at birth for persons born in the United States can be…

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Q: 7. If the rate of growth of a bacteria population is modeled by r(t) = 8e2t-1 thousand bacteria per…

A: Introduction: When a function is given, we determine the average value by integrating the function.…

Q: For the functiony = (x2 + 2)(x3 − 4x),at(−2, 0)find the following.(a) the slope of the tangent…

A: y = (x2 + 2)(x3 − 4x) = x5 + 2x3 - 4x3 - 8x = x5 - 2x3 - 8x Recall famous law of differentiation:…

Q: For the given curve y = 5x – 2x', when x increases at the rate of 2 units / sec, then how fast is…

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Q: The number of cell phone subscribers in a certain country in the early 2000s was projected to follow…

A:

Q: a drug concentration curve is given by C(t)= 20te^-0.2t, which C in mg/ml and t in minutes. What is…

A: A drug cocentration curve isC(t)=20te-0.2tTo find the rate of concentration. We have to…

Q: The rate of change of the population of a certain town is given by R(t) = 50e0.05t, where t is the…

A: The rate of change of the population of a certain town is given by R(t) = 50e0.05t, where t is the…

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: At time t=U years, a ranch has a population of 25 deer If the rate of growth of the population is…

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Q: A stuntman estimates the time T, in seconds, for him to fall x meters, 15. is T(x) = 0.54Vx. Find…

A: Instantaneous rate of change – It is the rate of change at each instant in time, not over a long…

Q: Use f(x+0.0001)-f(C) 0.0001 f(x)=52²-7x ata = 2, to the nearest tenth. to determine the…

A: Given function f(x)=5x2-7x

Q: if the rate of growth of the population of deer in a forest is modeled by R(t)= 2000e^(0.23t) deer…

A: The rate of growth of the population of deer in a forest is modeled by R(t)= 2000e(0.23t) deer per…

Q: Given the function g(x)=x² −2x³ +1, a. Estimate the instantaneous rate of change at x = 1. b. Will…

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Q: 7. If f (t) = -t2 + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

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Q: Given the function f(x) = x which of the following is a valid formula for the instantaneous rate of…

A: The given function fx=x23 The instantaneous rate of change is given by limh→0fa+h-fah