The concentration of a chemical agent in the bloodstream t hours after consumption is given by C(t)=  t / (50 + t3) What is the rate of change after 1 hour? Round to the nearest hundredth.

Q: The rate at which bacteria multiply is proportional to the instantanous N numbers present. If the…

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Q: Find the average rate of change of g(x) = - 3x + 4 from x = – 4 to a = 1. -

A: Given gx=-3x3+4We have to find average rate of change from x=-4 to x=1when…

Q: The area of a rectangle with one of its sides s is A(s) = 10s". What is the rate of change of the…

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Q: A balloon is deflating at a constant rate of 12 cm3 per second. When the volume of the balloon is…

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Q: The area of a rectangle with one of its sides s is A(s) = 6s². What is the rate of change of the…

A: Differentiate both sides of the equation, with respect to s to establish a relation between the…

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

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Q: The average births per woman in a country is modeled g(x) = 0.003x²- .18x +3.3 where x is the number…

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Q: What is the rate of change of f (t) at t = 7.5?

A: The rate of change is calculated using differentiation. The derivative of f(t) at t=7.5 gives the…

Q: Find the equation of the graph and estimate the instantaneous rate of change at x = 1

A: From graph we can conclude that the equation of this graph be a parabola i.e., a quadratic equation.…

Q: The number N of bacteria in a culture after t days is modeled by N= 400 [1 - 3/(t2+2 }2].Find the…

A: Given: The number N of bacteria in a culture after t days is modeled by: N=4001-3t2+22 To find the…

Q: The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. How fast is…

A: We have to find

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: A radioactive substance decays in such a way that the amount left after t years is given by A=100e…

A: Follow the procedure given below.

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: The number of Bacteria at time t hours is N= 1000 30 + te а. What is the initial number of bacteria…

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Q: The area of a square is decreasing at a rate of 158 square centimeters per second. At the time when…

A: Area of square =(side)2 perimeter of square = 4(side) let side of square= x cm

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: Find the average rate of change of h (x) = 2x² – 7x from x = 3 to r = 6. Simplify your answer as…

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Q: 14. Find the rate of change of y= (2x' +6x +4) at x =-1.

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Q: The area of a circle is decreasing at a constant rate of 181 square centimeters per second. At the…

A: Solution -  Here in this problem it is given that  Area of the circle decreasing at a constant rate…

Q: The number N of bacteria in a culture after t days is modeled by N= 400 [1 - 3/(t2+2 }2].Find the…

A: We have to use chain rule of differentiation. According to chain rule of differentiation , the…

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

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

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

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Q: The number of bacteria at the beginning of an experiment was 30 and the bacteria grow at an hourly…

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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: 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: The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. How fast is…

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

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

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Q: What is the instantaneous rate of change of S(t) 12 months from now? Round to 2 decimal place.…

A: Given, S(t) = 0.03t3+0.5t2+2t+3 Instantaneous rate of change is S'(t) S'(t) = ddt0.03t3+0.5t2+2t+3…

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

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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: A5.5-foot-tall woman walks at 4 ft/s toward a street light that is 16,5 ft above the ground, What is…

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Q: The area of a square is decreasing at a rate of 49 square inches per second. At the time when the…

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Q: Find the average rate of change of g (x) = 2x²-9x from x=2 to x = 6. Simplify your answer as much as…

A: The  average rate of change of function f(x) from the point x=a to x=b is given by:-    (f(b) -…

Q: Find the average rate of change of g (x) = 2x - 8x from x=2 to x= 6. Simplify your answer as much as…

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Q: D. Diego walks at the rate of 5 ft per second toward a street light whose lamp is 20 ft above the…

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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: If f(x) = 12x2 − x3, what is the rate of change of f '(x) at  (−1, 13)?

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Q: The area of a square is increasing at a rate of 56 square meters per minute. At the time when the…

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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: 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: The quantity (in grams) of a radioactive substance present after t years is Q(t)=100e-0.421t. Find…

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Q: The rate of change of the concentration of a bacteria culture is given by R(t) =80/ln2 (2)t, where t…

A: Given

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

A: NOTE: Refresh your page if you can't see any equations. . the given function is  take derivative

Q: The blood pressure P measured in millimeters of mercury of an adult x years old is given by P(x) =…

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