Find the rate of change of a population of size P(t) = ť + 4t + 6 at time t = 3. %3D

Q: Find the rate of change of the fucntion f(t)=4t^2-5t-3,[x,x+h

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Q: Let B = 5 T as in Example 3. Estimate the instantaneous rate of change of B with respect to T when…

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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: 9. The growth in the population of a group of rabbits is given by P(t) = 800e008 , where P is the…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

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

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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: 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: 2. Find the average rate of change of g (x) = -2x-2x from x= 1 to x=4. Simplify your answer as much…

A: Given, gx = -2x2-2x  We have to find the average rate of change of function from x = 1  to  x = 4 .…

Q: Find the rate of change of x with respect to p. 4 x2 0 0.000001x2 + 0.09x + 5 dx dp ||

A: Proceed as shown below

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: 4x+2 find average rate of change from x=-1 t x=1

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Q: 4. A beach ball is deflating at a constant rate of 10 cubic centimeters per second. When the volume…

A: NOTE: You have posted multiple questions we have given answer to the first question if there is a…

Q: Find the instantaneous rate of change of 7. y = (x + 1)*(x – 3) at a = 1.

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Q: S(2) = 32+-4 ant line to f(2) (ak.a, the average rate of change of ) from input val

A: Please refer to the image below

Q: 5. Find the instantaneous rate of change of the value function V in terms of t and N(t).

A: To find the instantaneous rate of change of the value function V in terms of N we will find dVdN…

Q: A population of 500 bacteria is introduced into a culture and grows in number according to the…

A: Given: pt=5001+4t50+t2 we know that population growing rate is given by differentiation of given…

Q: A triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant.…

A: Solved below

Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: dx 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: The radius of a sphere decreases at the rate of 4 m/s. when the radius is 10m, then the rate of…

A: We will find the rate of change in surface area as following .

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

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Q: What is the instantaneous rate of change of y=√√zat z=2? 0 ม O - O none of the above 0

A: The function is given by y = x To evaluate: The instantaneous rate of change of the function at x=2.

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

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Q: 10 If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does S g'(x)dx…

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

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

A: The surface area S of the body related to the body's weight W is given by S=kW2/3…

Q: tan(Cx) Va6+2 find the rate of change of P with respect to x, where C is a Given that P = constant.

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Q: 2. Find the instantaneous rate of change for y= arctan- at x = 3. 2 12 A. 85 2 В. 13 3n D. 4 С. О

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Q: 10. A cylinder is being filled such that the height of its contents is increasing at a rate of 5 cm…

A: Rate of change of height = 5 cm/s Volume, V = πr2h Radius, r = 3

Q: The rate of change of the number of coyotes N(t) in a population is directly proportional to 650 −…

A: Consider N(t) as the population of the coyotes after t years. Consider the given statement as the…

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

A: Find the second derivative of P

Q: The value of a computer t years after purchase is V(t) = 2, 000e-0.35t dollars. At what rate is the…

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

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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: The radius of a sphere decreases at the rate of 5 m/s. when the radius is 6m, then the rate of…

A: First I have written about rate of decrease in radius and then written the formula of Surface Area…

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: 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.…

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Q: With an initial deposit of 400 dollars, the balance in a bank account after t years is…

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Q: (a) The rate of change of P is proportional to N. When t = 0, N = 250, and when t = 1, N = 400. What…

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Q: 13. (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

A: (a) The average rate of a function f between the points a and b is given by: The area of a circle…

Q: The length of a rectangle is increasing at a rate of 9 in./s, while its width is decreasing at 2…

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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: The radius of a sphere is decreasing at a rate of 2 centimeters per second. At the instant when the…

A: Write the equation of the surface area of sphere solve it as per given in step 2

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.