A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2 hours there are 100 bacteria. When will the population reach 500?

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Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

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Q: Consider a tank with volume 100 liters containing a salt solution. Suppose a solution with 2…

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

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

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

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

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

A: Let's find.

Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into…

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

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

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Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Given: Rate of increase in length of a rectangle, dldt=5 cm/s Rate of decrease in width of a…

Q: Suppose the water in Example 4 is poured in at the rate of cubic inches per second. How fast is the…

A: Below is the solutions:-

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

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Q: There are currently 250 cells in a culture and it grows ata rate proportional to its size. After one…

A: Given data: Total cells=250 After one hour=630

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

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Q: nown to grow at a rate proportional

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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: At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

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

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Q: A tank contains 40 L of solution containing 2g of substance per liter. Salt water containing 3g of…

A: Initially there is 40*2 = 80 grams Let Q be the amount of substance in the tank and dQ/dt be the…

Q: The area of a rectangle remains 30 cm2. One side of the rectangle is expanding at a rate of 1 cm/s.…

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

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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 volume of a cube decreases at a rate of 0.3 3ft/min. What is the rate of change of the side…

A: Let the length of each side of the cube be a ft. Find the volume of the cube. Differentiate the…

Q: The number of bacteria in a liquid culture is observed to grow at a rate proportional to the number…

A: We know that at the beginning of the experiment, number of cells = 104 After 3 hours of the…

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,…

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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 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 radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

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

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Q: Sand flows out of an hourglass at a rate of 4 cubic inches per second and forms a conical pile. How…

A: Write the expression for volume of cone take the derivative with respect to time t than put the all…

Q: A tank contains 40 liters of a chemical solution prepared by dissolving 80 g of a soluble substance…

A: Given that, A tank contains 40 liters of a chemical solution prepared by dissolving 80 g of a…

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

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

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

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

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

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Q: A 30 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: Volume of the tank is 30 m3 The tank is full of brine with 40 kg of dissolved salt. Pure water…

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.

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

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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.