A bacteria culture starts with 1000 bacteria, and after 2 hours the population is 2500 bacteria. Assuming that the culture grows at a rate proportional to its size, find the population after 6 hours.

Q: A mold grows at a rate proportional to its present size. Initially there is 2 oz of this mold, and…

A: Let size of mold at time t is yt then according to given condition dydt α yt⇒dydt=kyt where k is…

Q: consider a tree with a tr

A:

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

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: The population of community is known to increase at a rate proportional to the number of people…

A:

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

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: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A: When length is:= 5 ft; When width is:= 2 ft; Rate of increasing length= 3 ft/s; Rate of increasing…

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: A substance cools in moving air at a rate proportional to the difference between the temperature of…

A:

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

A: Given that 10 years the population has trembled and for  20years the population is 150000. p(t)…

Q: A yeast grows at a rate proportional to its present size. If the original amount doubles in two…

A: Let v(t) be size of yeast at t time Therefore, ds/dt  ∝ s(t) ds/dt  = ks   [k is proportionality…

Q: A bacteria decreases at a rate of 15% continuously when exposed to ultraviolent light. If a culture…

A:

Q: A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced…

A:

Q: A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping…

A: Given ,dydt=-2ft/s     negative sign because as ladder is slipping down, y decreasesby Pythagor…

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: 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: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

Q: Water is flowing into a cylindrical tank at the rate of 2 m^3/min. If the radius of the tank is 0.5…

A: Water is flowing into a cylindrical tank at the rate of 2 m3/min.If the radius of the tank is 0.5 m,…

Q: A population of 1000 students are in a dormitory. If initially, a virus infected 25 of them. If the…

A: Let number of students infected at time t be x  Then, number of healthy students at time t = (1000 -…

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: Bacteria grown in a certain culture increase at a rate proportional to the amount present. If there…

A: This question is based on application of diffrential equation.

Q: In a chemical reaction a substance decomposes at a rate proportional to the amount of substance…

A:

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

A: The amount remaining after hours 24 hours is 88.5 milligrams.

Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

A:

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 population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

A:

Q: A bacteria culture is known to grow at a rate proportional to the amount present. If the population…

A: This is a problem of the application of differential equations.

Q: The population of a district in a town is known to increase at a rate proportional to the number of…

A: We will find out the required initial population of the state .

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

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

A:

Q: A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 2…

A: Given Data: The initial population of bacteria is: P0=260 The population of bacteria after 2 hours…

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

A:

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A:

Q: A certain population of bacteria is known to grow at a rate proportional to the amount present in a…

A: Solve for bacteria after 20 hrs

Q: The growth rate of a bacteria culture is proportional to the number of bacteria present. If a…

A:

Q: It is known that a bacterial culture increases at a rate that is proportional to its current amount.…

A: Given- Number of bacterial fibers after 1 hour=1000 Number of bacterial fibers after 4 hour=3000

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

A:

Q: Initially 100 millions of radioactive substance was present. After 6 hours the mass has decreased by…

A: Given query is to find the amount of radioactive substance after 24 hours.

Q: A certain population of bacteria grows at a rate that is proportional to the number present. It is…

A: Given that: Growth rate of bacteria ∝ Number of bacteria presentNumber doubles in 2 hr

Q: Initially 87 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A: We know that the differential equation of the decaydAdt=kAwhere A = amount and k = proportionality…

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A:

Q: A puppy weighs 2.0 lb at birth and 3.5 lb 2 months later. If the weight of the puppy during its…

A:

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

A:

Q: A culture of bacteria grows at a rate that is proportional to the present number. It is found that…

A:

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

A:

Q: 2. The population of a country doubles in 50 years. How many years will be 5 times as much? Assume…

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.