It is known that a bacterial culture increases at a rate that is proportional to its current amount. 1000 bacterial fibers were observed in the culture after 1 hour and 3000 fibers after 4 hours. Accordingly, initially find the number of fibers in the culture.

Q: The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: Given that rate of decay of radium is proportional to the amount present at that time.

Q: The bacteria in a culture can be assumed to multiply at a rate that at any given moment is…

A:

Q: The number of insects in a colony is known to multiply at a rate proportional to the number of…

A:

Q: Initially 35 grams of radioactive substance was present. After 5 hours the mass had decreased by 11…

A: Given:- Initially 35 grams of radioactive substance was present. After 5 hours the mass had…

Q: Initially 50 grams of radioactive substance was present. After 6 hours the mass had decreased by 9%.…

A:

Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: Initially 56 grams of radioactive substance was present. After 8 hours the mass had decreased by 6%.…

A: Let's find.

Q: The population of a state is known to grow at a rate proportional to the number of people presently…

A: Follow the steps.

Q: A spherical drop of liquid evaporates at a rate proportional to its surface area. If a given drop…

A:

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

A: Given that , The radioactive material is known to decay at a rate proportional to the amount…

Q: A certain population of bacteria grows such that its rate of change is always proportional to the…

A:

Q: Initially 100 milligrams of a radioactive substance were present. After 6 hours the mass had…

A:

Q: In the absence of predators the population of mosquitos in a certain area would inccrease at a rate…

A: Let P(t) be the population of mosquitoes in the area with t in weeks, and k be the rate at whichthey…

Q: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

A: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

Q: The population of a certain municipality increases at the rate proportional to the present…

A: Here we solve the given population growth problem.

Q: Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square…

A: Let,

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

A:

Q: As part of the process in the production of a perfume, a certain substance with water is converted…

A: We have to formed a differential equation and solve it get amount converted or amount left

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

A:

Q: If

A: Explanation and solutions is given below....

Q: The rate of change of the male population of a particular barangay is proportional to the male…

A:

Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

A:

Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

Q: nown to grow at a rate proportional

A:

Q: Initially 50 grams of radioactive substance was present. After 10 hours the mass had decreased by…

A: The rate of change of amount A with respect to time t can be denoted by dAdt. If x is directly…

Q: Initially 42 grams of radioactive substance was present. After 5 hours the mass had decreased by 8%.…

A: Initial mass of radioactive substance is equals to 42 g after five  hours mass is decreased by 8%

Q: Initially there was 80 milligrams of radioactive substance present.  After an 8 hour period the mass…

A: From the differential equation from the given information. dPdt=kPdPP=kdt Here, the amount of…

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: A wet towel hung from a clothesline to dry loses moisture through evap-oration at a rate…

A:

Q: A certain population of bacteria doubled after 20 minutes. If it is known that it grows proportional…

A:

Q: Suppose an unknown radioactive substance produces 800 counts per minute on a Geiger counter at a…

A:

Q: Suppose that the magnitudes of two earthquakes differ by 1 on the Richter scale. Find the ratio of…

A: Earthquake A be the larger earthquake and earthquake B be the smaller one. The difference in the…

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

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

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

A:

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

A:

Q: The kinetic energy of an object varies jointly with its mass and the square of its velocity. What…

A: let: Kinetic energy be k Mass be M. Velocity be V The kinetic energy is directly proportional to…

Q: A cup of coffee cools at rate proportional to the difference between the constant room temperature…

A:

Q: A tank contains 400L of fresh water. By mistake, 100kg of salt is poured into the tank instead of…

A:

Q: Initially 48 grams of radioactive substance was present. After 6 hours the mass had decreased by…

A:

Q: Initially 47 grams of radioactive substance was present. After 10 hours the mass had decreased by…

A:

Q: An apple pie with an initial temperature of 170 -C is removed from the oven and left to cool in a…

A:

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

A: In mathematics, two varying quantities are said to be in a relation of proportionality,…

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

A:

Q: A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They…

A: Given that initial number of fish is 100 and rate of increase of population of fish is directly…

Q: Initially 25 grams of radioactive substance was present. After 10 hours the mass had decreased by…

A:

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

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.