The amount in grams in a sample of uranium-239 after t years is given by A(t) = 100e -0.36t (a) Find the rate of change of the amount. (b) Find the rate of change of the amount present after 3 years. Include units in your answer.

Q: Snowballs formed by kids in winter season is found to melt in such a way that the rate of change in…

A:

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: Find the rate of change. Cube root 3√x with respect to x when x = 1, 8, 27

A: Consider the given: fx=x3ddxfx=ddxx3ddxfx=ddxx13ddxfx=13x13-1ddxfx=13x23

Q: The area of a square is increasing at a rate of 36 centimeters squared per second. Find the rate of…

A:

Q: The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by f'(t) =…

A:

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

A:

Q: A vehicle purchased for $32500 depreciates at a constant rate of 4%. Determine the approximate value…

A: Solving

Q: The area of a square is increasing at a rate of 56 centimeters squared per second. Find the rate of…

A: Given data÷ Rate of change of area  =dAdt=56cm2/s Side of square =a=4cm We need to find dadt=?

Q: (a) Find the instantaneous rate of change of pressure with respect to temperature if the temperature…

A: Question is solved.

Q: The United States population (in millions) is predicted to be P(t) = 317e0.01t,  where t is the…

A: Given: The United States population (in million) is predicted to be P(t) = 317 e0.01t, where t is…

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: The number N of bacteria in a culture after t days is modeled by N= 400 [1 - 3/(t2+2 }2].Find the…

A: Given: The number N of bacteria in a culture after t days is modeled by: N=4001-3t2+22 To find the…

Q: Find the average rate of change of g (x) = -x* +4x+2 from x = 3 to x = 7. Simplify your answer as…

A: See picture added

Q: The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. a) What is the…

A: Applications of derivatives

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

A:

Q: what is the rate of change of the circumference of the circle?

A:

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: The number N of bacteria in a culture after t days is modeled by N= 400 [1 - 3/(t2+2 }2].Find the…

A: Given: The number bacteria in a culture after t days is, N=4001-3t2+22.

Q: The number N of bacteria in a culture after t days is modeled by N= 400 [1 - 3/(t2+2 }2].Find the…

A: We have to use chain rule of differentiation. According to chain rule of differentiation , the…

Q: The rate of decomposition of radioactive radium is proportional to the amount present at any time.…

A: The rate of decomposition is proportional to y, we know that y=Cekt, where t is the time in years.…

Q: Based on the graph above, estimate (to one decimal place) the average rate of change from x=1x=1 to…

A:

Q: The body mass index (BMI) is a number that can be calculated for any individual by using the…

A:

Q: Outside of the box question: The number of treated mosquitoes increased from 20 to 2000 within 8…

A: Rate of change of mosquitoes

Q: The area of a square is increasing at a rate of 80 centimeters squared per second. Find the rate of…

A: Given,         The area of a square is increasing at a rate of 80 centimeters squared per second.

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

A: Given that , h=48 inch r1=3 feet , r2=5 feet find average rate of change in volume.

Q: The United States population (in millions) is predicted to be  P(t) = 317e0.01t,  where t is the…

A: Given: Pt=317e0.01t we know that for finding instantaneous rate of change of the population in the…

Q: Sue rode her bike at a constant speed, travelling 10km from Aurora to King City in 0.5h. was the…

A:

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

A:

Q: At a temperature of 20°C, the volume V (in liters) of 1.33 g of o, is related to its pressure p (in…

A: As per guideline we have to solve one question Please repost other question again

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

A: Given fuction

Q: The sides of a cube increase at a rate of K cm/s. When the sides have a length of 2 cm, the rate of…

A:

Q: The area of a square is increasing at a rate of 64 centimeters squared per second. Find the rate of…

A:

Q: I just put a new rain barrel to catch the rain that falls on my roof. It started raining at 10:50…

A: Given Data: The starting time of rain is: T1=10:50 am The observation time is: T2=12:15 pm The…

Q: 3. The amount of pollution x miles downwind of an electrical plant is g (x) = 64x¬4 + 8x parts per…

A:

Q: The area of a square is increasing at a rate of 16 centimeters squared per second. Find the rate of…

A: Given,        The area of a square is increasing at a rate of 16 centimeters squared per second.…

Q: A5.5-foot-tall woman walks at 4 ft/s toward a street light that is 16,5 ft above the ground, What is…

A:

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

A:

Q: Use a numerical example to explain the difference between the rate of change and the level of change…

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: 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: It started raining at 10:15 am, and by 12:10 pm the barrel had 7 inches of water in it. What was…

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: The percent concentration y of a certain drug in the bloodstream at any time t (in hours) is given…

A: Our objective is to find the derivative and derivative at t=1

Q: . The voltage,V, in a circuit is slowly dropping at a rate of -0.01 volt/sec as the battery wears…

A: I have appended the formula used in the solution part.

Q: The number N of bacteria in a culture grewat a rate proportional to N. The value ofN was initially…

A:

Q: If a ball is dropped from a height of 2304 feet, then its height in feet above the ground is given…

A: Given that, if a ball is dropped from a height of 2304 feet, then its height in feet above the…

Q: The quantity (in grams) of a radioactive substance present after t years is Q(t)=100e-0.421t. Find…

A:

Q: 2.) An underwater drone is being used to explore ancient ruins at the bottom of the ocean. begins at…

A:

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.