Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved. Initially, 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left. How much time will it take until 90% of the sugar is dissolved?

Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved. Initially, 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left. How much time will it take until 90% of the sugar is dissolved?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

See similar textbooks

Related questions

Q: 4. A 105 kg male needs to work at a MET level of 8 to reach his target heart rate. If he exercises…

Q: Assume that the rate of evaporation for water is proportional to the amount of water in a bowl. If…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Given by If Palladium has a half-life of of 4 days then the model is: A = A0(1/2)(t/4) We are given…

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: To solve the following problem and find the amount of water left at 6:10pm.

Q: The surface area of kelp near Monterrey Bay is 40,000 square acres, but after four years a red sea…

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

Q: A radioactive substance has a half-life of 64 hours. If 200 grams of the substance are initially…

Q: The rate at which radioactive nuclei decay is proportional to the number of nuclei that are present…

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Suppose…

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

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: Given: The amount of water at 3:56 PM is 10452 L and amount of water at 4:12 PM on same day is 8092…

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Given , half-life of Palladium-100 is 4 days t1/2=4 days Let N(t) be the quatity after t days…

Q: 3. Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of…

A: Given: initial mass of Radium y0=96 mgWe know that General decay equation is y=y0e-kt…

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: Model the given problem dpdt=kp if p is the present number of bacteria integrate it on both sides…

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Given :Half life of Palladium-100= 4 days

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

Q: After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is present.…

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Given : The half life of Palladium-100 is 4 days and after 24 days a sample of Palladium-100 has…

Q: An isotope of cesium has a half life of 29 years. If 1300 grams of cesium disintegrates over a…

Q: A certain radioactive material loses mass at a rate proportional to the mass present. If the…

Q: A tank contains 1,000 gal of brine in which 500 lb of salt are dissolved. Fresh water runs into the…

A: Form the first order differential equation and solve using separation of variables.

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

Q: Assume that a snowball melts so that its volume decreases at a rate proportional to its surface…

A: Let V denote the volume and A denote surface area. Rate of melting is proportional to its surface…

Q: The half-life of plutonium-241 is approximately 13 years. How much of a sample weighing 4 g will…

A: The half-life of plutonium-241 is 13 years. We have to find how much sample of 4 g will remain after…

Q: There are 100 bacteria cells in a dish now, but in 5 hours there will be 147 cells. At what rate do…

A: There are 100 bacteria at initial time t=0. In 5 hours that is when t=5, there will be 147 cells. In…

Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Each side of a square is increasing at a rate of 6 cm/s. To determine the rate at which the area of…

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

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Consider the decay of Palladium-100, The half life of Palladium-100 = 4 days and after 24 days…

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 190 years? Lead-210 decays at a…

A: Here initial amount A0=4000g Decaying rate λ= 3.15% = 0.0315 Let amount remains in 190 years= A(t)

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

Q: A tank contains 5000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

Q: Radium decomposes at a rate proportional to its present radioactive. In 100 years, 100 units of…

Q: A radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of radium…

Q: A mold grows at a rate proportional to its present size. If the original amount doubles in one day,…

Q: A piece of machinery valued at $30,000 depreciates at a rate of 10% yearly. How long will it take…

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

Q: a certain radioactive material is known to decay at a rate proportional to the amount present. if…

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A: Topic-basic maths

Q: 1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is…

A: Give: Area of base is A=20 ft2 Rate with which tank is filling dVdt=0.5 ft3/min. Volume of a…

Q: An element with mass 310 grams decays by 8.9% per minute. How much of the element is remaining after…

A: Given mass = 310 gm Rate = 8.9 % Time = 19 min

Q: The number of germs in a certain culture increases at a rate proportionai to the number present. If…

A: Given that, the number of germs in a certain culture increases at a rate proportional to the number…

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

Q: In a chemical reaction, a certain compound changes into another compound at a rate proportional to…

A: Let y be the unconverted amount of substance A at time t. Thus, the given information can be written…

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

Q: An element with mass 430 grams decays by 27.4% per minute. How much of the element is remaining…

A: We need to find the exponential function representing the decay of the element.

Q: The number of germs in a certain culture increases at a rate proportional to the number present. If…

Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

Q: 1. After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is…

Concept explainers

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.

Question

100%

Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved. Initially, 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

How much time will it take until 90% of the sugar is dissolved?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

The half-life of magnesium-27 is 9.45 minutes. How much of a 10-mg sample will be left in 6 minutes?
The half-life of a radioactive material is about 34.2 years. How much of the material is left after 20 years?
Researchers recorded that a certain bacteria population declined from 700,000 to 400,000 in 5 hours after the administration of medication. At this rate of decay, how many bacteria will there be 24 hours from the start of the experiment?
The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?