Pollution levels in a lake have been modeled by the equation x = 0.04 + 0.17e−0.38t where x is the volume of pollutants (in cubic kilometers) and t is the time (in years). What is the rate of change of x with respect to time? x'(t) =

Q: 1. Find the instantaneous rate of change when x=π for y=sin*x/2-3cosx.   2. Interpret geometrically…

A: Simply take the derivative and put the given point to find the instantaneous rate of change.

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.03 cm/ min.…

A:

Q: There was a girl in a class studying math with, of course, a math teacher. This girl's name is…

A: Given query is to find the amount converted in two hours.

Q: Find the rate of change of 1/x with respect to x when x=2

A: f(x)=1xrate of change of 1/x with respect to x isdf(x)dxdf(x)dx=-1x2

Q: Water in a cylindrical container with radius 8 cm and height h is leaking at a rate of 20 cm³ per…

A:

Q: the rate of change of the population of a city is proportional to the population P at any time t…

A:

Q: Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and…

A: Given problem:- Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a…

Q: Water is running into a hemispherical bowl having a radius of 10 cm at a constant rate of 3 cu.…

A: Calculus Question

Q: e first derivative for the +1)(x +2) 2)

A: Find the first derivative. y=(x+1)(x+2)(x-1)(x-2)

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. The most…

A: Given that the brightness of the Delta Cephei at time t( in days) has been modelled by the function…

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 radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the…

A: Given: dQdt=-rQ for Q is the amount present at time t. 100 mg reduce to 82.04 mg in 1 week, the…

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att= 0, fresh…

A:

Q: A Cepheid variable star is a star whose brightness altermately increases and decreases. For a…

A:

Q: A tank contains 2220 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the…

A:

Q: Carbon decays at a rate proportional to the amount present. The percentage lost is 5% in 150 years,…

A: Given: Carbon decays at a rate proportional to the amount present. The percentage lost is 5% in 150…

Q: 2. A tank with a shape of a cone is 20 feet deep and has a diameter of 10 feet at the top. Water is…

A: Given; Diameter = 10 feet  Height = 20 feet

Q: The length l of a rectangle is decreasing at the rate of 2 cm/sec while the width w is increasing at…

A: Given:The length of rectangle is decreasing at rate 2cm/sec  The width  of rectangle is…

Q: The length of a rectangular box is increasing at 3 in/sec, while its width is decreasing at 4…

A: Differentiate volume of rectangular box wrt t

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

Q: 2. A light shines on top of a lamppost 30 feet above the ground. A woman 5 feet tall walks away from…

A: Let X be the distance of man from lamppost .

Q: A roast turkey is taken from an oven when Its temperature has reached 185F and Is placed on a table…

A: Follow step 2.

Q: Pollution levels in a lake have been modeled by the equation x = 0.08 + 0.18e−0.35t where x is the…

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: Consider a function y = 1 / x a) Find the rate of instantaneous change of y with respect to x at x…

A: a) y = 1 / x dy / dx = - 1 / x2

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: Given that rate of decay is proportional tp the current amount x.So,dxdt=kx,    where k is…

Q: The radius of a cylindrical tube is increasing at a rate of 2 meters per hour, and the height of the…

A: Cylinder is a figure with circular base with a certain height. We can see it as the below diagram.…

Q: IfI represents the intensity of light which has penetrated water to a depth of x feet, then the rate…

A:

Q: Molar volume is a function of temperature and the pressure or V = f (T, P) ; and its total…

A:

Q: Initially, 10 grams of a radioactive substance were found in a sample. It was observed In z that 20%…

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: 2. The length () of rectangle is decreasing at the rate of 2 cm/sec while the width (w) is…

A: Given Length of rectangle is decreasing at the rate of 2cm/sec⇒dldt=-2cm/secwidth is increasing at…

Q: It is known that a bacterial culture increases at a rate that is proportional to its current amount.…

A: Given- Number of bacterial fibers after 1 hour=1000 Number of bacterial fibers after 4 hour=3000

Q: Empirical evidence suggests that the volume V (measured in liters) of a kangaroo's pouch depends on…

A:

Q: Sand pouring from a container forms a conical pile whose height is equal to the diameter. If the…

A: Note: According to our guidelines we can answer only 5th question

Q: A boat is sailing at 1 meter per second towards a cliff that rises 281 meters above water level. Let…

A:

Q: The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x…

A:

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.05 cm /…

A: Area =πr² Find dA/dt when r=56 cm

Q: potter forms a piece of clay into a cylinder. As she rolls it, the length, L, of the cylinder…

A: Given problem:- A potter forms a piece of clay into a cylinder. As she rolls it, the length, L, of…

Q: The horizontal distance or range (R) of an object thrown at an angle 8 from the horizontal is…

A:

Q: Find the rate of bubble volume increasing when the radus is 4cm if its surface area is increasing at…

A: Given: dSdt=4  cm/secdVdt|r=4 cm=?

Q: Graphically, the instantaneous rate of change of a function at a specific x-value can be estimated…

A: Given: The below four statements are given: (a)Determining the slope of a single secant line on the…

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: A culture initially has N0 number of bacteria. At time t = 1 hour the number of bacteria is measured…

A:

Q: 2. The volume and radius of a right circular cylinder change at the rates of 1 cm^3/s and -2 cm/s,…

A: Given : Radius = 2cm, height = 1 cm Rate of change of radius is 2 cm/s and rate of change of volume…

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

A:

Q: If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: An emply container is filled with liquid. The height of the liquid in the container is x cm and its…

A:

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases.The most…

A: The rate of change of a function f(t) is the first derivative of f(t) with respect to t.

Q: A hot object is placed in a room whose temperature is 69°F. After 1 minute the temperature of the…

A:

Exponential Growth Model

The relation that represents an exponential function is: