The population of a town is modelled by P(t)= 6t +110t +3000 , where P is the population and t is the number of years since 1990. Find the average rate of change in population between 1995 and 2005.

Q: The time rate of change of an alligator population P in a swamp is proportional to the square of P.…

A:

Q: If a person's temperature after x hours of strenuous exercise is T(x) = x3(7 x2) + 98.6 degrees…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm²/min, find the decreasing…

A: To find- Radius is decreasing at the rate of

Q: Find the average rate of change of g(x) 5æ – 5 from x = - 3 to a = 3.

A:

Q: For the function f (x) = a-5a2. (a) Evaluate the average rate of change from r = -2 to r 1 (b) What…

A: Given, The function fx=x3-5x2 We have to solve for part a and b

Q: Find the average rate of change of g (x)=x-4x+1 from x 2 to x 6. Simplify your answer as much as…

A: Given data: The given function is g(x)=x2-4x+1. The lower limit of x is a=2. The upper limit of x is…

Q: Find the average rate of change of g(x)= -3x^3 +4 from x=-2 to x=3

A:

Q: A police car traveling south toward Sioux Falls, Iowa, at 160km/h pursues a truck traveling east…

A: Given that a police car is travelling south toward Sioux falls at 160km/hour and  a truck is…

Q: Given the function g(x) = -x² – 5x + 8, determine the average rate of change of the function over…

A:

Q: Q5 Find the instantaneous rate of change at 2 for: f(x) = 6x2-9x -6

A: The given function is,

Q: The rate of growth of a fish population was modeled by the equation G(t) = 60000e−0.5t/(1 +…

A: The answer is found in step-2.

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

A: The given function is gx=-2x2-3x and the given points are x=-2 and x=3. When the value of x=-2, the…

Q: Find the average rate of change of f(x) = - 3x2 + 5 from 3to 7

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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: Given the function h(x) = x² + 10x + 21, determine the average rate of change of the function over…

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: Given the function h(x) = x² – 7x + 6, determine the average rate of change of the function over the…

A: The rate of change of a function is given by it's derivative.

Q: Given the function h(x) = x2 + 10x + 21, determine the average rate of change of the function over…

A: The objective is to determine the average rate of change of the given function.

Q: Determine the instantaneous rate of change at x = 3 for g(x) = x² − 2x+5. A. 2 B. 4 C. 6 D. 8

A:

Q: A population of bacteria is growing according to the equation P(t)=850e0.22tP(t)=850e0.22t. Estimate…

A:

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

A:

Q: A population of a small city had 3000 people in the year 2000 and has grown at a rate proportional…

A: In this question, we will use growth topic of differential equations.

Q: Q 4 Find the average rate of change between 5 and 0 for: f(x) = 6x2 -9x - 6

A: Obtain the average rate of change of function as follows:

Q: Find the average rate of change of g(x) = – 2x³ 1 from x = - 1 to r = 4.

A:

Q: Let the height of an object bef(t)=t2+2t−4f(t)=t2+2t−4. What is the instantaneous rate of change of…

A: Given query is to find instantaneous rate of change of the object at t = 2.

Q: Given f(x) + 4x + 2, find the average rate of change on the interval [1, 3].

A:

Q: If a person's temperature after x hours of strenuous exercise is T(x) = x³ (7- x²) + 98.6 degrees…

A: We have to calculate the rate of change after 1 hours

Q: A factory is dumping pollutants into a river at a rate given by dx/dt = t3/4/600 tons per week,…

A: First we separate the variables

Q: An oral medication is absorbed into the bloodstream at the rate of 7e−0.04t milligrams per minute,…

A: An oral medication is absorbed into the bloodstream at the rate of 7e-0.04t.

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: Given the function f(x) = –x² – 5x + 12, determine the average rate of change of the function over…

A:

Q: Given the function f(x) = -x² – 7x + 19, determine the average rate of change of the function over…

A: Given function is: fx=-x2-7x+19 And the given interval is: -9≤x≤3 At x=-9:…

Q: Given the function f(x)=4^x-2 , explain and show how to find the average rate of change between x=2…

A:

Q: Find the average rate of change of f(x)=4x^2-2 from 2 to 4 

A: For the function f(x) the rate of change in a closed interval a to b is given (f(b)-f(a))/b-a Here,…

Q: Given the function f(x) = -x²+ 3x + 8, determine the average rate of change of the function over the…

A:

Q: Given the function g(x) = -x² + 6x + 11, determine the average rate of change of the function over…

A:

Q: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

A:

Q: What is the rate of change for h(x) = 2x2 + 7 on the interval [2, 9]?

A:

Q: Find the average rate of change of g (x) = 2x - 8x from x=2 to x= 6. Simplify your answer as much as…

A:

Q: Given the function f(x) = -x² – 7x + 15, determine the average rate of change of the function over…

A: Given, fx=-x2-7x+15 over the interval -9≤x≤3 To find the average rate of change.

Q: The table gives the profit, P of a fast food chain, where P is in millions of dollars and t is in…

A: Given,

Q: For the function y = 5x3- 4x a. Determine the average rate of change between x1 = 3 and x2 = 5.  b.…

A: given function y=fx=5x3-4x

Q: Given the function h(x) = -x² – 6x + 11, determine the average rate of change of the function bver…

A: The average rate of change of a function, y=f(x) over the interval, a, b is calculated using the…

Q: The rate of growth of a fish population was modeled by the equation G(t) =…

A: Consider the given: Gt=90000e−0.6t1+5e−0.6t2

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: find the average rate of change of g(x)= -2x3 +5x2 from x=-1 to x=2 simplify your answer as much as…

A:

Q: Given the function g(x) = -x2 – 3x +5, determine the average rate of change of the function over the…

A:

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…

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.