12 6. Suppose that f (t) = 3t + 2 a. What is the average rate of change of f(t) over the interval 2 to 4? b. What is the instantaneous rate of change of f (t) when t = 2?

Q: A rate of change of H is given by = k(5+ H). When t = 0, H = 4. When t = 3, H dt = 10. Solve for…

A: Given :

Q: Suppose that f(t) = 3t + 2 – 12t. а. What is the average rate of change of f (t) over the interval 2…

A: We are given the function f(t) = 3t+2-12t => f(t) = 2-9t. For (a), The average rate of change of…

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Q: Let g(x) = 2x² + 5x + 1. Find a value of c between 1 and 7 such that the average rate of change of…

A: Solve for c

Q: Consider the following function. 1 f(x) Find its average rate of change over the interval [4, 16].…

A: Given:  fx=1x  To Find:  The average rate of change of the function over the interval 4, 16=?…

Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

Q: Suppose the population of a colony of ants grows at the rate P'(t) = 1 +   5 /(√ t + 1)   If…

A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

Q: A company estimates that its revenue grows continuously at a rate given by R'(t)= 2e^2t, where t is…

A: By Using simple integration

Q: 2. If f(t) is the rate of change of some quantity, then what does f (t) dt represent?

A:

Q: 9. The rate at which the value, V, of a painting changest years after it is completed is given by…

A: Image is attached.

Q: Suppose the height of a spacecraft at time 1 is given by f () = 27 E1 for 0 <15 3. Find an…

A:

Q: 2.1 Suppose that f (t) = 3t + 2 – 12t. а. What is the average rate of change of f(t) over the…

A: Given : f(t) = 3t + 2 - 12t To find : a. What is the average rate of change of f(t) over the…

Q: 1. A honeybee population starts with 100 bees and increases at a rate of f'(t) bees per week. What…

A:

Q: 4. Which of the following functions grows at the same rate as ex as x goes to infinity? ex+3 e3x e2x…

A: We find which of the following functions grow at the same rate as ex as x goes to infinity: (1) ex+3…

Q: |81. Recall that the present value (PV) of an investment that pays out income continuously at a rate…

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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: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: suppose that g(s)=s^2+3s+4 . find a value c in the interval [0,2] such that g'(c) equals the average…

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Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

Q: Consider the following function. g(x) = x³ – 5 Find its average rate of change over the interval…

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Q: Let F(s) = 5s² + 2s + 4. Find a value of d greater than 0 such that the average rate of change of…

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Q: A population of E. coli bacteria will grow at a rate given byw′(t) = (3t + 2)1/3,where w is the…

A: Given: w't=3t+21/3

Q: 3. Assume that the level of nitrogen dioxide present in the atmosphere on a certain June day in city…

A: The level of nitrogen dioxideN(t)=0.05t3t-64+53  0≤t≤8

Q: If f(x) = 5x-3 Compute the instantaneous rate of change of f(x) at x = 2. OA.7/41 Ов. -3/49 Oc. 1/5…

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Q: Suppose that f(t) =t+4t-4. W.at is the average rate of change of f(t) over the interval 3 to 4? %3D…

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Q: Suppose that D = √x² + y² is the length of the diagonal of a rectangle whose sides have lengths x…

A: To find the formula for the rate of change of D with respect to x, differentiate D=x2+y2, using the…

Q: at the rate of r (t) = 3t liters per minute, where t is the time in Which of the following defines a…

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A: Given function is Differentiating both sides with respect to x, we get

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A: Given, Qt=-t3+6t2+24t a. Compute the worker's rate of production at 11:00 A.M. Here t=3 ( Difference…

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Q: Suppose that f(t) =t +t-5. What is the average rate of change of f(t) over the interval 4 to 5? The…

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Q: Consider the following function. g(x) = x³ – 5 Find its average rate of change over the interval…

A:

Q: Q2 The rate of heat transfer of a body can be express as: dT = -k(T – Ta) dt where T= temperature of…

A: Using Euler's method we can find the solution, the initial values are t0 = 0 and T0 = 90°C The…

Q: 19. Suppose the rate of change of production of a regular worker at a factory is given by dp…

A: Given problem:- Suppose the rate of change of production of a regular worker at a factory is given…

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

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Q: 2 Refer to the graph above and without making any computa- tions find: The average rate of change…

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Q: 1)™ Determine a formula for the derivative of (x° + that works for any integer m. m y'

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Q: A pump allows water to flow into a pool at the rate of r (t) = 2t liters per minute, where t is the…

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Q: Suppose h(t) = t² + 11t + 7. Find the instantaneous rate of change of h(t) with respect to t at t =…

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Q: 5. If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet t seconds later…

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Q: -4 to x = 1 Find the average rate of change of g(x) = 3x° - 1 from z =

A: Average is (g(1) -g(-4)) /5

Q: Consider the following function. 1 f(x) Find its average rate of change over the interval [1, 4]. Ду…

A: Solve the function

Q: 9. The derivative of the graph x+y² D5 with respect to time is c-2y+ 20 C. a. y +x d. -y 2x +2y

A: Q 9 Given that: The graph: x2+y2=25

Q: Consider the following function. f(t) = 2t2 – 1 Find the average rate of change of the function…

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Q: 3. If f (t) = -t² + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A: Given : The function ,ft=-t2+5t+3 describes  the distance travelled by the ball in meters. To find:…

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

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Q: If f(x) = 5x -3 , compute the instontoneus rate of change of Sx) at x-2. OA -3/49 O8.7/41 oc-7/41…

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Q: 4. Suppose that the population of a certain collection of rare Brazilian ants is given by P(t) = (t…

A: Recall: Rate of change of P(t) is dP(t)dt. d(tn)dt=n.tn-1 d(u.v)dt=u.dvdt+dudt.v

Q: 2. The instantaneous rate of change of g(x) is the same for every real value of x. What conclusion…

A: