It started raining at 10:15 am, and by 12:10 pm the barrel had 7 inches of water in it. What was the average rate of change of the height of the water during this time period? Answer:    inches/minute If the rain kept falling at this same, constant rate, when would the rain height in the barrel reach 16 inches?

Q: As illustrated in the figure, a car is traveling along one road, away from the intersection, at 10…

A:

Q: The area of a square is increasing at a rate of 9 square inches per second. At the time when the…

A: We are asked to find the rate of change of the perimeter of the square

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

A: Solving

Q: A freshly brewed cup of coffee has temperature 95°C in a  20°C room. When its temperature is 70°C,…

A: Given that, Initial temperature of coffee is T0=95°C, surrounding temperature is Ts=20°C. Also,…

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: Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west…

A:

Q: A kite 30 meters above the ground moves horizontall at At what rate is thelength of the string speed…

A:

Q: A freshly brewed cup of coffee has temperature 95 ° C in a 20 ° C When its temperature is 70 ° C it…

A: The temperature of a freshly brewed coffee is 95°C and the temperature of the room is 20°C. When the…

Q: The volume of a cube decreases at a rate of 0.75 ft3 of the side length when the side lengths are 15…

A: Given the volume of a cube decrease at a rate of 0.75 ft3/min. To find the rate at which the side…

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: It started raining at 10:35 am, and by 11:45 am the barrel had 8 inches of water in it. What was the…

A: NOTE: Refresh your page if you can't see any equations. . x=time (in minutes) after 10:35 am y=water…

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: The gross domestic product (GDP) of a certain country was N(t) = t² + 5t + 106 billion dollars t…

A: This is application of derivative so take the derivative and than put the value of time t.

Q: To determine drug dosages, doctors estimate a person’s body surface area (BSA) (in meters squared)…

A: Solution:Given     BSA=hm60To calculate  the rate of change of BSA with respect to mass for a person…

Q: The area of a square is decreasing at a rate of 158 square centimeters per second. At the time when…

A: Area of square =(side)2 perimeter of square = 4(side) let side of square= x cm

Q: If a new Mustang is valued at $20,000 and five years later it is valued at $8000 then what is the…

A: A new Mustang is valued at $20,000 and five years later it is valued at $8000. Let x be the year and…

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A:

Q: If ω'(t) is the rate of growth of a child in pounds per year,what does  ∫510 ω'(t)  dt   represent?

A:

Q: The area of a circle is decreasing at a constant rate of 181 square centimeters per second. At the…

A: Solution -  Here in this problem it is given that  Area of the circle decreasing at a constant rate…

Q: 3. A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above…

A:

Q: A balloon is 30 meters above the ground when a car, running at 40 kph, passes directly below it. It…

A: Given,         A balloon is 30m above the ground when a car, running at 40kph passes directly below…

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: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: Consider the given situation, Let the length of the rectangle be ‘l’ and breadth be ‘b’.Area of…

Q: Suppose that y = C(t) represents the average cost of a gallon of milk in the United States t years…

A: represents the change in the average cost of a gallon of milk in the United States t years since…

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: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

A:

Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Here we have a population of fruit flies that changes at a rate of g(t)=-4e0.04t…

Q: The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of…

A:

Q: The number N of bacteria in a culture after t days is modeled by 3 N = 500 1 (1? + 2)2 Find the rate…

A: N=5001-3t2+22

Q: ) An environmental study estimates that t years from now, the level of carbon monoxide in the air of…

A: Given that :-the level of carbon monoxide:Q(t)=0.01t3+0.1t+2.2 ppm.Q(5)=0.01(5)3+0.1(5)+2.2…

Q: from the edge of a cliff into described by the function ht rate of change in the height - 4.9t² +…

A: Formula average height change=(h(b)-h(a))/(b-a) Where a=4second b=5second

Q: ending from the surface. What is the best estimate of its instantaneous change in depth at t = 3 sec

A: In this question, the concept of the derivative is applied. Derivative A derivative is used to…

Q: A vehicle purchased for $29800 depreciates at a constant rate of 8%. Determine the approximate value…

A: cost price of vehicle=$29800 Constant rate of depreciates =8% per year We have to find the…

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: How are the rate constant and the doubling time related?

A: Explanation: The exponential growth function is y(t)=y0ekt where k  is the positive constant rate…

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: The area of a square is decreasing at a rate of 49 square inches per second. At the time when the…

A:

Q: If a new car is valued at $20,600 and 8 years later it is valued at $3000​, then what is the average…

A: Given that the value of a new car is $20,600 and 8 years later it is valued $3,000.The initial value…

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing…

A: topic - application of derivatives

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: given that the area of a triangle(A)=140cm2 altitude(h)=20cm dh/dt=1cm/min dA/dt=2cm2/min let the…

Q: In an experiment, the population of C of a certain type of a bacteria int hours, is given by... C(t)…

A:

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 66°C, it…

A:

Q: A jet is approaching a radar station with a speed of 1,256 mph and a stable altitude of 9504ft. When…

A:

Q: With an initial deposit of 400 dollars, the balance in a bank account after t years is…

A:

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: Given 100 grams of bacteria that decreases at a rate of 1/2 per year. What would be an appropriate…

A: Initial value: 100, Rate: 1/2 per year(decreases). So, the population equation is p(t)=100e-12t…

Q: what is the average rate of change of f(x)=log2(x) between 4 and 32. write the answer as a fraction

A: It is average rate of change.

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

A:

Exponential Growth Model

The relation that represents an exponential function is: