A coal-burning electrical generating plant emits sulfur dioside into the surrounding air. The concentration C(a), in parts per million, is approximately given by the function 0.9 C(2) = where ar is the distance away from the plant in miles. The instantaneous rate of change of the sulfur dioxide concentration (to four decimal places) 3 miles from the plant is parts per million per mile.

Q: Find the instantaneous rate of change for function at the given value. F(x) = x2 + 2 at x = 0

A: Given a function, F(x) = x2 + 2 at x = 0 To Find the instantaneous rate of change for function at…

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A:

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: 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: If l represents the intensity of light which has penetrated water to a depth of x feet, then the…

A:

Q: The air in a room with volume 180 m3 contains 0.15% carbondioxide initially. Fresher air with only…

A:

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

A:

Q: Find the instantaneous rate of change for the function at the given value. f(x) =x + 4x at x= - 4…

A: NOTE: Refresh your page if you can't see any equations. . to find the instantaneous rate of change,…

Q: The fungus Fusarium exosporium infects a field of flax plants through the roots and causes the…

A:

Q: The time it takes an average athlete to swim 100 meters freestyle at age x years can be modeled as…

A: please see the attachment

Q: A triangle base is increasing at a rate of 4 cm/s and its height is decreasing at a rate of 1 cm/s…

A:

Q: A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The…

A: Given C(x) = 0.3/x^2 Therefore, Derivative of C(x) = 0.3 (-2)(x^-3) = -0.6/x^3

Q: A radioactive substance decays in such a way that the amount left after t years is given by A=100e…

A: Follow the procedure given below.

Q: find the rate of change. The reciprocal 1/x with respect to x when x = 1, 2, 3

A: The rate of change of a function is the value of the derivative of the function; thus, let the…

Q: The time it takes an average athlete to swim 100 meters freestyle at age x years can be modeled as…

A:

Q: Assume that the rate of change of air pressure with altitude (distance above the earth) is…

A: Topic:- Differential equation

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

A: The surface area S of the body is related to the body's weight W according to S is:

Q: 3. fox =V X at X T6

A:

Q: Given the function f(x)= X x-2’ a. Determine the average rate of change on the interval -4≤x≤-1. b.…

A:

Q: If x is measured in months where x=0 represents January of 2000, and F(x) represents the US GDP…

A: given GDP is measured in  millions of dollars  x is measured in months

Q: 5. The concentration of a drug in the bloodstream t hours after the injection is given by is the…

A: C(t)=4.35 e-tRate of change of concentration;dCdt=ddt(4.35 e-t)dCdt=-4.35 e-tRate of change after 1…

Q: Find the instantaneous rate of change for the function at the given value. f(x) =x+3x at x= - 1 The…

A:

Q: A colony of fruit flies grows at a rate proportional to its size. At time t = 0, approximately 20…

A: Let the population of fruit flies be modelled by function y.  The question mentions that the rate is…

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate (in…

A: Let the diameter be D cm and radius be r cm  The surface area S of the the sphere in term of…

Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

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

A:

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: The growth in the population of a group of rabbits is given by P(t)= 800e0.08t, where P is the…

A: use derivative for finding the instantaneous rate

Q: Find the instantaneous rate of change for each function at the given value: F(x)= x2 + 2 at x = 0

A: Given: F(x)= x2 + 2 at x = 0

Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A:

Q: (13) The blood pressure P measured in millimeters of mercury of an adult x years old is given by…

A: Given: P(x)= 40+25ln (x+1)  the limit 0 between 65 To find : Rate of change  of pressure of the…

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A: Given: dPdt=0.071P, r=7.1% and initial amount invested is P0

Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A:

Q: Find the instantaneous rate of change for the function at the given value. f(x)=x + 2x at x= 0 The…

A:

Q: Suppose that the spread of a disease through the student body at an isolated college campus can be…

A: Here we have to find out rate of change of y.

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: estimate the instantaneous rate of change at the point indicated. f (x) = e^x ; x = 0

A: To find the instantaneous rate of change at x=0 we need f'(0) So we find f'(x)

Q: A certain radioactive substance is decaying so that at time t, measured in years, the amount of the…

A:

Q: Find the instantaneous rate of change of g(x)=(x^3-sqrt(x))e^x+(x^5-2x+3)ln(x) when x=3. Round to…

A: The instantaneous rate of change of g(x) is:…

Q: The time it takes an average athlete to swim 100 meters freestyle at age x years can be modeled as…

A: Given:The time it takes an average athlete to swim 100 meters freestyle at age x years can be…

Q: The value of y varies at a constant rate of change of 1.7 with respect to x. If x varies from x=3 to…

A:

Q: The drug concentration in the bloodstream t hours after injection is given approximately by C(t)=…

A: Ct=4.95e-t, 0≤t≤5

Q: Suppose a pollutant is seeping into the ground near a dump site at the rate of 7200 f(t) (* + 1.5)"

A:

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A: Given dpdt=0.068P

Q: find the instantaneous rate of change of the function at the given x-value. f(x)=x2 + 3x at x=4

A: f(x)= x2+3x  and x=4

Q: Find the instantaneous rate of change for the function at the given value f(x) =x +2x at x= 0 The…

A:

Q: The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x2 + 10x + 5000. What is…

A:

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: When the interest on an investment is compounded continuously, the investment grows at a rate that…

A:

Q: Given the function f(x) = x which of the following is a valid formula for the instantaneous rate of…

A: The given function fx=x23 The instantaneous rate of change is given by limh→0fa+h-fah

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.