Find the rate of change of a population of size P(t) = t + 2t + 6 at time t = 2. The rate of change of a population of size P(t) = ť + 2t + 6 at time t = 2 is i

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: We found that salt is added to the tank at a constant rate and it is removed from the tank at a rate…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: What is the amount of salt in the tank at time t = 0?

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Q: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2…

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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%…

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Q: When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of…

A: Consider the approximation cost of goods. Ct=p1.05t Rate of change of C=dCdt. So, Differentiate the…

Q: Alice measures a radioactive sample at 1400 counts/minute on a Geiger counter. If the radioactive…

A: Given: Initial value, R0=1400 counts/min Ending value, R = 1000 counts/min Time that has passed, t =…

Q: A culture initially has P number of bacteria. At t = 3hour the number of bacteria is measured to be…

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Q: 5. If the population P of bacteria (in units of 1000) is declining because of a toxin, its rate of…

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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: Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y =…

A: The formula for average rate of change from a to b is : f(b)-f(a)b-a

Q: A population of bacteria can be modeled by the function f(t)=1000(0.98)t where t represents the time…

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Q: For the function y = 4x2: (a) Find the average rate of change of y with respect to a over the…

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Q: With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate…

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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: 1. For function f (x) = 0.5*, state a) the average rate of change from x = -1 to x = 1 b) the…

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Q: a. A tank holds 1000 liters of water, in which 15 kg of salt is dissolved. Pure water enters the…

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Q: Estimate the instantaneous rate of change of P(t)=3t^2− 6 at the point: t =

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Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: Suppose that a community contains 15,000 people who are susceptible to Michaud’s syndrome, a…

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Q: Find the maximum rate of change of f(s,t)= te^{st} at the point (0,5).

A: In this question we have to find the maximum rate of change.

Q: The rate of change of x is proportional to x. When t = 0, x0 = 3 and when t= 2, x = 6. What is the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: 2-t-1 Find the average rate of change of z(t) = on the interval between t= 1 and t=2. 2 -t+3

A: The average rate of change of z(t) in the interval t=1 and t=2 is given by:

Q: Determine the instantaneous rate of change of the function y = 5x + 2x² 1 with respect to x at x-4.…

A: Find instantaneous rate of change

Q: With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate…

A: ∫xndx = xn+1n+1 + C, where 'C' is the constant of integration.

Q: 18. Estimate the instantancous rate of change of the function f(x) = x' +4x - 11x-30 at x = 1. Round…

A: Given,  f(x)=x3+4x2-11x-30, x=1

Q: The base x of a triangle is decreasing at the rate of 5 in./sec. and the height y of the triangle is…

A: Given Base = x  Height = y Rate of change of base = dx/dt = - 5 in/s Rate of change of height =…

Q: Find the rate of change of x with respect to p. p =  9 0.000004x2 + 0.05x + 8,    x ≥ 0

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Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: What is the rate of change of y with respect to x for 9x-11y+2=0

A: Given that 9x-11y+2=0 We need to find the rate of change of y with respect to x that is dy/dx.

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: 9. Suppose an object is moving along a path described by; f(t) = t - 6t, where f (t) is measured in…

A: The objects velocity at t is equal to 4 will be the objects instantaneous rate of change at that…

Q: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

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Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

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Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

A: Integrating a population growth rate between a to b that is ∫abRatedt

Q: A culture initially has P0 number of bacteria. At t=3 hour the number of bacteria is measured to be…

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Q: Find the rate of change of x with respect to p. p= 9/0.000004x2 + 0.05x + 8, x ≥ 0   dx dp

A: We need to find first derivative of given equation with respect to p

Q: Consider a tank that initially contains 100 gallons of a solution in which 50 pounds of salt are…

A: Here I am attaching image so that you understand each and every step.

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: A certain population of bacteria grows at a rate that is proportional to the number present. It is…

A: Given that: Growth rate of bacteria ∝ Number of bacteria presentNumber doubles in 2 hr

Q: How would I solve for the left endpoint and the right endpoint? Find the average rate of change of…

A: Given :f(t) = 4t2 − 3,      [3, 3.1] formula for average rate of change :

Q: The population of Normal, Illinois grows proportionally to its population at time t. At an initial…

A: Given, dPdt=kP Where P is the population and k is the proportionality constant.

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

A: Given: y=lnx at x=1

Q: Find the rate of change of x with respect to p. p= 9/ 0.000004x2 + 0.05x + 8 ,  x ≥ 0

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Q: (a) A cougar was found dead in the woods by a ranger, which he assumed was shot by a poacher. The…

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Q: z = x2 + y2, where x and y are increasing at the constant rates of 2 units per second and 3 units…

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