Suppose the rate of sales of a new product is given by f(t) = 200 – 90e-t, %3D where t is the number of days the product is on the market. Find the total sales during the first 5 days.

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…

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

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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: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

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Q: 5. Find the instantaneous rate of change of 1 g(x) = 2x – 32x° + 17x² – 9x + 4 at x = 2

A: Given equation is, gx=2x4-32x3+17x2-9x+4

Q: Suppose C(t) is the cost, in thousands of dollars, of producing t tons of white paper. If  C'(10) =…

A: Given:C(t) is the cost of producing t tons of white paper.It is known that,

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

A:

Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the instantaneous rate of change of f(x) at x = 2.

A: Given function is

Q: In some chemical reactions, the rate at which the amount of a substance changes with time is…

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

Q: After the introduction of foxes on an island, the number of rabbits on the island decreases by 4.5%…

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: Explained below

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: 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: For a certain manufacturer, the revenue obtained from the sale of q units of a product is given by…

A:

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

A:

Q: Find a real number a such that the instantaneous rate of change of the function flx) =2x²+ 4x+7 at x…

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

A: The given function,   g(x)=x2+2x+2 from x=2 to x=7

Q: If the average test score (in percent) of a group of math students at IMU is given by p=100-5ln(3t…

A:

Q: Find the average rate of change of g(x) 2x 5 from x – 1 to r = 4.

A:

Q: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

A:

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

A:

Q: An investment of 6,000 grows at a rate of 4% for one year, then at a rate of 9% for three years.…

A: Investment amount = 6000 Rate of return for first year = 4% Rate of return for three years = 9% * 3…

Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 140 when p = $5…

A: Here, dxdp=10p-5⇒dx=10p-5dp⇒∫dx=10∫1p-5dp+C...(1)

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

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

A:

Q: Suppose that y = C(t) represents the average cost of a gallon of milk in the United States t years…

A: represents the change in the average cost of a gallon of milk in the United States t years since…

Q: Find the average rate of change from x 2 to x-2+ h for the function f()and simplify so that no…

A: we have to find average rate of change of f(x) between [2+h,2] using formula mentioned above

Q: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

A: Area = length x width A = L x W

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

A: We can find the average rate of change of a function as below in the following steps.

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 length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

A: Given, length of rectangle is increasing at a rate of  7 cm/s width of rectangle is increasing at a…

Q: The weekly cost C, in dollars, for a manufacturer to produce q automobile tires is given by C = 2100…

A: Rate of change of cost function is the derivative of cost function with respect to time .

Q: 1.A culture has y,number of bacteria. At time t=2 hours, the number of bacteria is measured to be…

A: Given, Initial number of bacteria is y0. also, given at time t=2 hours, the number of bacteria is…

Q: If f'(t)=2t is a production rate, measured in items per hour, then how many items were produced from…

A:

Q: Assume the rate of investment is given by the function I (t) = ln t. Compute the total capital…

A: We solve this problem by using the capital formation i. e. Total capital accumulation=∫t,t2I(t)dt…

Q: If f(x) = 5x2 − x3, what is the rate of change of f '(x) at (2, 12)?

A: To calculate the rate at which the given function changes at the given point

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 f(x) = 3x-8x from x 1 to x = 6. Simplify your answer as much as…

A: average rate of change=  f(b)−f(a)/b−a a=1 b =6 f(x) = x(3x -8) f(a) = 1(3-8) = -5 f(b) = 6(18-8) 60…

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

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Q: Suppose a pollutant is seeping into the ground near a dump site at the rate of 7200 f(t) (* + 1.5)"

A:

Q: A certain radioactive substance has a half-life of 50 hours. Find how long it will take for 90% of…

A:

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: 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: If f(x) = −2x^3 + 5 what is the average rate of change between x = −1 and x = 4

A: Use formula of avg rate of change

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: C'(10) = 380,

A: Given: Suppose C(t) is the cost, in thousands of dollars, of producing t tons of white paper. If…

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5V9x2 –…

A:

Q: Find the average rate of change of g(x) = 4x° – 1 from x = - 1 to x = 1

A:

Q: Find a formula for the average rate of change of f (x) = x^3 over [2, x] and use it to estimate the…

A: We use the average rate of change formula