Bacteria grow in culture at a rate proportional to the amount present. Initially, 300 strands of the bacteria are in the culture and after two hours that number has grown by 20%. Find the time needed for the bacteria to double its initial size.

Q: . A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the…

A: Using mixing problem formula we find the general amount of salt at any time t minutes and then…

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: Initially 71 grams of radioactive substance was present. After 4 hours the mass had decreased by 9%.…

A:

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

A:

Q: A tank contains 52 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Please see the answer below

Q: A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a…

A: Let x represents the amount of salt after t minutes. Given that, the initial amount of salt is 15…

Q: A bacteria culture starts with 1000 bacteria, and after 2 hours the population is 2500 bacteria.…

A:

Q: A tank contains 60L of water contaminated with Mercury at a concentration of 0.03 mg/L. Clean water…

A: Here we need to find and then solve the differential equation for the concentration of mercury using…

Q: A population of mosquitoes increases at a daily rate of 1/2 times the current population. You can…

A: Given that A population of mosquitoes increases at a daily rate of 1/2 times the current population.…

Q: A population of cattle is increasing at a rate of 800 + 80 t per year, where t is measured in years.…

A:

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

A: From the rule of decay that is, the rate of decay is proportional to the amount of the substance…

Q: A 20 m tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: In this question, we find the amount of solt when the takl half full. given that  Initial amount of…

Q: A tank contains 57 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A:

Q: A swimming pool is nearly​ empty, holding only 5100 gallons of water. A system is set up so that the…

A:

Q: I am having trouble solving this.

A: Let V be the volume at any time t. Hence, dV/dt α V1/3 Or, dV/dt = kV1/3 where k is the factor of…

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: A tank contains 48 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A:

Q: A population of bacteria grows at a rate proportional to the number of bacteria at the time. There…

A: Given that:                      Bacteria growth rate is proportional to the number of bacteria at…

Q: 6. The amount of pain reliever in Tony's bloodstream decreases at a rate that proportional at any…

A: Let amount of pain reliever in Tony's bloodstream be x Given  dxdt=-kx

Q: A swimming pool is nearly​ empty, holding only 5100 gallons of water. A system is set up so that…

A: The number of gallons p in the pool after x hours can be written as: p(x)=5100×1.17x Take the…

Q: A tank contains 45 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: image is attached

Q: The number N Iinsects in culture grew at a rate proportional to N. The value of N was initially 100…

A:

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

A:

Q: A large tank holds (400) gallons of brine solution with (50) pounds Q5: of salt. A concentration of…

A:

Q: A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A:

Q: A tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

A:

Q: Radium decomposes at a rate proportional to the amount present at any instant. If initially there…

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: In the first few weeks after birth, a baby gains weight at a rate proportional to its weight. A baby…

A: Introduction: Differential Equation packages are beneficial in each educational and realistic…

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: A tank contains 200 liters of fresh water. Brine containing 2 kilograms per liter of salt enters the…

A:

Q: The substance decomposed at a rate proportional to the amount resent. What is the half-life of the…

A:

Q: A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the tank…

A:

Q: A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: A tank contains total solution 60 gallons Compose of 85% water = 51 gallons And 15% alcohol = 9…

Q: The population of Tagum City is increasing at the rate proportional to its current population. In…

A:

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: Radium decomposes approximately at a rate proportional to the amount present. If 100 g now will be…

A:

Q: A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

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: A tank contains 50 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Consider the given information. Let y is the number of gallons of alcohol in the tank with rate of…

Q: tially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds of salt…

A:

Q: how long will it take $800 to triple if it is invested at an annual intrest rate of 5.3%

A: P=$800 , R=5.3%

Q: A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Given ,  A tank contains 60 gallons of a solution composed of 85% water and 15% alcohol. A second…

Q: The number N Iinsects in culture grew at a rate proportional to N.The value of N was initially 100…

A:

Q: Brine containing 1.5 lb/gal of salt enters a tank at the rate of 2 gal/min and the mixture…

A:

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

A: Initial radium quantity Ni = 100 mg after t = 100 years N = 96 mg

Q: A wet towel hung on a clothesline to dry outside loses moisture at a rate proportional to its…

A:

Q: A partially filled tank with 100 gallons of water in which there are 10 pounds of dissolved salt. a…

A:

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 tank contains 54 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Consider the given information. Let y is the number of gallons of alcohol in the tank with rate of…

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.