Media consultants for the new local magazine IT-Solutions! have projected that the number of sub- scriptions will grow during the first five years at a rate given by 1000 s'(t) = 0

Q: Five mice in a stable population of 500 are intentionally infected at r= 0 with a contagious disease…

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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: The cost of producing x units of a certain commodity is c(x) = 1000 +5.70x +.7x2. What is the…

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Q: Find the interest earned at 5% compounded continuously for 2 years by a continuous income stream…

A: Given the interest earned r=5%=0.05 , t=2years and PV=1250. We have to find the interest.

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: 2. Find the average rate of change of g (x) =x*-3x¯+2x from x=1 to x=3.

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Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: Estimate the instantaneous rate of change at the point indicated. f (x) = ex ; x = e

A: To find the instantaneous rate of change at indicated point:f(x)=ex;x=e. Solution: we know, the…

Q: (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not…

A: 3. given graph of function is                                                       Also,…

Q: 4.) The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x? + 10x + 5000.…

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Q: After ·t months, the production output at a certain factory is N (t) thousand units, where N (t) =…

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Q: volume

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Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rqa', in millirems per hour.…

A: Given: The rate of decay of a substance is given by, , where is a initial amount of substance.

Q: What is the rate of change of y = In x at x = 10?

A: Explanation: Given that,  y=lnx   Concept Used: To find the rate of change we will find the…

Q: 8. Create the equation of any function where the instantaneous rate of change when x = 1 does not…

A: Create the equation of any function where the instantaneous rate of change when x = 1 does not…

Q: Suppose a liquid is to be cleared of sediment by pouring it through a cone-shaped filter. Assume…

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Q: Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always two…

A: The radius is 2 times the height, the rate at which the height increases is 3 cm/s when the pile is…

Q: Suppose that $15,000 is invested and at the end of 3 yr, the value of the account is $19,356.92. Use…

A: Given :            $15,000 is invested and at the end of 3 yr, the value of the account is…

Q: The area of the expanding rectangle is increasing at the rate of 48 square centimeters per second.…

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Q: Suppose y varies at a constant rate of change of 4 with respect to x (so that Δy=4⋅Δx ), and when…

A: topic - linear equation in two variables

Q: What are three methods that can be used to estimate the instantaneous rate of change in g(x) at x =…

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Q: You are a process control engineer in a water purification plant. In a certain subprocess, water…

A: Mathematical methods used to solve equations or evaluate integrals or solve differential equations…

Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

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Q: What is the concentration of glucose in the bloodstream after 10 min if r =5 g per min, k = 5, and…

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Q: Estimate the instantaneous rate of change of P(t) = 2t² – 6 at the point t = - 2 |

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Q: If the average rate of change of a function between x = a and x = b is negative, then is the…

A: The rate of change of function between two points of a curve represents the slope of the curve.   If…

Q: When air expands adiabatically (without gaining or losingheat), its pressure P and volume V are…

A: Pressure and Volume are related by equation At a instant

Q: 1. Suppose that oil spills from a container and spreads in a circular pattern. If the radius of 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: Suppose the amount of oil pumped from one of canyon near the beach of island decreases at the…

A: Given query is to find the time when output will become one fifth of initial value.

Q: D. Supposes a circle is expanding in such a way that its radius is growing at a constant rate of 3…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the…

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Q: approaching

A: Please refer to the image below

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: You are a process control engineer in a water purification plant. In a certain subprocess, water…

A: Given that the flow is maintained such that qi-q0>0 and their difference is the product of the…

Q: After a foreign substance is introduced into the blood, the rate at which antibodies are made is…

A: Please see the below picture for detailed solution.

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rọa“, in millirems per hour.…

A:

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: Estimate the instantaneous rate of change of the function f(x)=2x^2−1 at x=1 using the average rate…

A: The given function is,

Q: 1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles…

A: As per our guidelines we are supposed to answer only one question. I am solving the first one Kindly…

Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

A: Given that, The half-life of a radioactive material whose rate of disintegration is proportional to…

Q: Find the average rate of change of g(x) 2x + 6 between x = 1 and x = 4 -

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Q: Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1…

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Q: What is the rate of change of y = In x at x = 1 O?

A: Given: y=lnx at x=1

Q: A 60-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 Ib…

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Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

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Q: Find the average rate of change of from y = x³ - 2x + 3 from 0 to x = 3. -

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

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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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.