If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then  means

Q: Find the rate of change of the fucntion f(t)=4t^2-5t-3,[x,x+h

A:

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

A: Given: g(x)=4x3-4

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Given that ,    Ecologist estimate that, when the population of a certain city is x thousand…

Q: Because of the absence of predators, the number of rabbits on a small island increases at a rate of…

A: Given that the growth function is: y(t) = y0ekt. At, t=0, y(0) = y0 [This is the initial…

Q: For the function y = x2 , find the instantaneous rate ofchange of y with respect to x when x = 3.

A: The instantaneous rate of change of y with respect to x is given by dy/dx

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: ologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Answer

Q: What is the rate of change for h(x) = 8x - 9 on the interval [1, 4]?

A:

Q: What is the rate of change of f (t) at t = 7.5?

A: The rate of change is calculated using differentiation. The derivative of f(t) at t=7.5 gives the…

Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the instantaneous rate of change of f(x) at x = 2.

A: Given function is

Q: Consider the function f (x) = x2. Calculate the rate of change of f (x) at x = 1, and compare your…

A: Consider the function f (x) = x2  To Calculate the rate of change of f (x) at x = 1.

Q: Find the average rate of change of g(x) = 2x° – 4 from x = - 1 to x = 3 -

A: This question is based on average rate of change of function.

Q: Given the function f(x)=x2/3, which of the following is a valid formula for the instantaneous rate…

A:

Q: If ,f(x) = 19x2 − x3, what is the rate of change of f '(x) at (2, 68)?

A:

Q: In the equation, x² +y² = 45, what is the value of the rate of change in y with respect to time t…

A:

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: If f(x) = 3x + 2x + 6, find the instantaneous rate of change of f(x) at x = 1. -

A: Topic - applications of derivativea Instantaneous Rate of change of f(x) at x is given by slope of…

Q: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate…

A: fx=x23fx+h=x+h23At x=8f8+h=8+h23f8=823=23×23=4

Q: 3. fox =V X at X T6

A:

Q: What is the rate of change of y with respect to x for this function?

A:

Q: Let  x(V) = V1/3  be the length of the side of a cube in terms of its volume. As V decreases, does…

A: V is decreasing that is dv/dt is negative  Let dv/dt =-k where k is constant.

Q: A population of bacteria can be modeled by the function f(t)=1000(0.98)t where t represents the time…

A:

Q: Where k is constant. If the temperature is increasing at 4 kelvins per hour, what is the rate of…

A: We need to find the rate of change of pressure  when temperature is 150K and pressure is 450…

Q: In the equation, x² + y² = 45, what is the value of the rate of change in y with respect to time t…

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: Suppose the constant rate of change y with respect to x is -2.5 and we know that y=-6.75 when x=1.5…

A: Given,The constant rate of change of y with respect to x = -2.5.We know that,Slope = rate of change…

Q: Find x0 given that the rate of change of y =2x2+x-1 with respect to x at x=x0 is 4

A: giveny =2x2+x-1 rate of change=4rate of change=dydxdydx=4x+1

Q: Determine the instantaneous rate of change of the function y = 5x + 2x² 1 with respect to x at x-4.…

A: Find instantaneous rate of change

Q: Find the rate of change of x with respect to p. 500 – X 0 < x < 500 8x

A:

Q: Based on the data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 5. Assume that an airplane is flying toward you at a constant height of 2 miles and at a speed of…

A: Here we solve this question using differentiation and basic trigonometric formulas.…

Q: estimate the instantaneous rate of change at the point indicated.f (x) = ln x; x = 3

A: To find the instantaneous rate of change at x=3 we need f'(3) We find f'(x)

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: Numerically estimate the instantaneous rate of change of f(x)=e-x^2

A:

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: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: Given,1f=1p+1qwhere f is focal lenrth and an object is placed at a distance p from the lens and its…

Q: If f(x) = 5x2 − x3, what is the rate of change of f '(x) at (2, 12)?

A: To calculate the rate at which the given function changes at the given point

Q: What is the instantaneous rate of change of A with respect to s when s is 4.00?

A: Given a square of area A in2 and length of the side s in To find the instantaneous rate of change of…

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

A:

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 average rate of change of g(x) 2x + 6 between x = 1 and x = 4 -

A:

Q: If f(x) = 12x2 − x3, what is the rate of change of f '(x) at  (−1, 13)?

A:

Q: Let H(t) be the amount of raw honey at time t. During processing, the amount of raw honey present…

A: We have to use exponential decay function to solve the problem

Q: A stuntman estimates the time T, in seconds, for him to fall x meters, 15. is T(x) = 0.54Vx. Find…

A: Instantaneous rate of change – It is the rate of change at each instant in time, not over a long…

Q: It follows from Poiseuille's Law that blood flowing through certain arteries will encounter a…

A: Given  R(x) = 0.25(1 + x)4

Q: Use f(x+0.0001)-f(C) 0.0001 f(x)=52²-7x ata = 2, to the nearest tenth. to determine the…

A: Given function f(x)=5x2-7x

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…

Q: Given the function g(x)=x² −2x³ +1, a. Estimate the instantaneous rate of change at x = 1. b. Will…

A: