rerage rate of change given g(x) = 4x – 3x + 5 from a = - 3 to z = 3:

Q: Q4) growth of a spherical tumor modeled as a function of the population of germs (g in Million) in…

A: As per our guidelines we are allowed to solve one question at a time . We will be solving the first…

Q: 3. The cost (in dollars) of producing x units of a certain commodity is. C()-100+50x-0.02x2 (a) Find…

A: a) To calculate the average rate of change of C(x) from x1 = 100 and x2 = 105.

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: the rate of change in thr profit (p) with respect to the number of units sold (x) is 0.0006x^2 +10.…

A: We can use the given equation to solve for profit

Q: A fish tank initially contains 40 liters of pure water. Brine of constant, but unknown,…

A:

Q: Initially 10 grams of salt are dissolved into 15 liters of water. Brine with concentration of salt 5…

A: In this question we have to find rate of change come of amount in salt

Q: 5. For y = -ln(x), find the value of x where the slope is a) x = − 6 b) -In(6) d) Does Not Exist

A:

Q: c) A cube has sides of length x cm and volume V cm3 . The volume is increaring at a rate of 1.5…

A: It is application of derivative.

Q: A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t=0,…

A: Given: the volume of swimming pool = 10000 gal that contains 0.03% chlorine. at t=0  ,0.002%…

Q: Boyle’s Law states that when a sample of gas is compressedat a constant temperature, the pressure P…

A:

Q: e population of a certain country is known to increase at a rate proportional to e number of people…

A: Topic:- population growth exponential function

Q: Q4) growth of a spherical tumor modeled as a function of the population of germs (g in Million) in…

A: Given function f(x), we can find the rate of change in f w.r.t to other variable t as dfdt=dfdxdxdt

Q: A bacteria culture starts with 460 bacteria and grows at a rate proportional to its size. After 5…

A:

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/ min.…

A: Topic:- application of derivatives

Q: A bacteria culture starts with 540 bacteria and grows at a rate proportional to its size. After 6…

A: Let present size of bacteria = x   Given bacteria grows at a rate proportional to its size  Rate of…

Q: dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at any…

A: Given query is to find the amount of solid after 1 second. f'(t) = -5f(t) (5+f(t)).

Q: 3. The point P(x, y) is moving along the curve y = x? -"x 10 +5x in such a way that the rate of…

A: Given: The point Px,y is moving along the curve y=x2-103x32+5x is such a way that the rate of change…

Q: A tank contains 100 gallons of brine containing 5 pounds of salt. Brine with a concentration of 2%…

A:

Q: If a tank holds 3500 gallons of water, which drains from the bottom of the tank in 50 minutes, then…

A: V = 3500 (1- t/50)^2 dv/dt = 140(1- t/50)     d) (dv/dt  t=50) =  140(1-(50/50)) = 0

Q: A bacteria culture starts with 580 bacteria and grows at a rate proportional to its size. After 3…

A: (a) Consider the given statement of the question,

Q: A small town is known to grow its population at a rate proportional to the population at any time.…

A:

Q: Range and height versus speeda. Show that doubling a projectile’s initial speed at a given launch…

A: Range of projectile is given by R=u2sin2θg Doubling the initial velocity, Range R'=2u2sin2θg = 4R'

Q: An oil tanker breaks apart and starts leaking. As time goes on, the rate at which the oil is leaking…

A:

Q: Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

A: Given Boyle's equation PV=C, where P is pressure , V is volume and C is constant. Also, given that…

Q: Q4) growth of a spherical tumor modeled as a function of the population of germs (g in Million) in…

A:

Q: at a constant 3. The surface area of a balloon being inflated changes a rate. If initially, its…

A:

Q: A pyramid has height h and a square base with side x. The volume of a pyramid is V = xh. f the…

A:

Q: An executive conference room of a corporation contains 4500 ft3 of air initially free of carbon…

A:

Q: A shallow reservoir has a one-square-kilometer water surface and an average water depth of 4 meters.…

A: Given the reservoir has one square kilo meter water surface and an average water depth of 4m.…

Q: A culture initially has Po number of bacteria. At t = 4hour the number of bacteria is measured to be…

A: We will find out the required doubling time.

Q: g(x) = 6/x+1 ; x = 0, x = h How do I find the net change and average rate of change between 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: how do you find the average rate of change of the function over the given interval? y = -3x3 + 2x2…

A: Calculation:The given function is y =  – 3x3 + 2x2 – 4x + 1. Let y = f(x).Substitute x = – 2 in the…

Q: Consider a tank used in hydrodynamic experiments. After one experiment the tank contains 200 L of a…

A: y=amount of salt at time t  ............the water is fresh

Q: he rate of change of monthly subscriptions to a new streaming TV service are expected to follow 1 S'…

A:

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

A:

Q: A water storage container starts leaking at time t = 0 minutes. The water leaks out from the…

A:

Q: A culture initially has Po number of bacteria. At t=1 hour, the number of bacteria is measured to be…

A: Given:  A culture initially has P0 number of bacteria. At t=1 hour, the number of bacteria is…

Q: 9. Sales for a speaker system have been growing at the rate: f'(t) = 2000(3 – 2e-t) systems/yr where…

A: We have to use definite integrals

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

A:

Q: Estimate the instantaneous rate of change of P(x) 5x-3 at the point r = 2 Your answer should be…

A:

Q: Q4) growth of a spherical tumor modeled as a function of the population of gems (g in Million) in…

A: For any function involving two variables or more, derivative can be found using any third variable…

Q: An oil tanker breaks apart and starts leaking. As time goes on, the rate at which the oil is leaking…

A:

Q: cube with edges of length x centimeters has volume V(x) - cubic centimeters The volume is increasing…

A: .

Q: 3 Find the average rate of change of the function f(x) , on the interval x E [-2,4]. 2 3x + Average…

A:

Q: A shallow reservoir has a one-square-kilometer water surface and an average water depth of 4 meters.…

A:

Q: Water flows into and out of a storage tank. A graph of the rate of change r(t) of the volume of…

A: To estimate the amount of water in the tank four days later by using Midpoint rule.

Q: A rectangle is expanding with time. The area of the rectangle is increasing at a rate of 12 cm2/min.…

A:

Q: The instantaneous rate of change for the function Y=x^2+2x,  at x= 3

A: The rate of change of any function is given by dydx  at any point x=x0 ,that is derivative of 'y'…

Q: An exponential fuction is given by the equation y=3^× Using the points x and x+1 show that the y -…

A:

Exponential Growth Model

The relation that represents an exponential function is: