A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the rate of 500 bacteria per day, how fast is the culture growing when it reaches 15,000 bacteria?

Q: suppose the population of a certain bacteria in a laboratory sample is 100. if it is doubles in…

A: Given: The population of a certain bacteria in a laboratory sample is 100 and it is doubles in…

Q: A radioactive substance decays at a rate proportional to the amount present, and half the original…

A: given radioactive substance that its half life is 1500 years. we have to find time after which the…

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

A: Given : S=the amount of radium you start with=250gm t=the amount of time in years=950 years  h=the…

Q: If the population of the earth was found to be 3.5 billion in 1970, and Is Increasing at a rate of…

A: The population of the earth was 3.5 billion in 1970,  We are to find at what year population of…

Q: The volume of a cube is decreasing at a rate of 24 cubic inches per minute. At the instant when an…

A: Given that  The volume of a cube is decreasing at a rate of 24 cubic inches per minute.…

Q: There are currently 100 cells in a culture and it grows at a rate proportional to its size. After…

A:

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 4.5 ft tall man is walking away from a 25 ft tall lamp post.  If he is walking at a rate of 2…

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

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

A: Here we solve the given population growth problem.

Q: A patient is adminstered a dose of 70mg of a drug. If the body naturally disposes of 5% of the drug…

A: Given,           A patient is administered a dose of 70mg of a drug and the body naturally disposes…

Q: An airplane, flying horizontally at an altitude of 1km, passes directly over an observer. If the…

A: Given: y = altitude = 1km  constant speed of plane dx/dt = 240kph

Q: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

A:

Q: In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the population had…

A: Given,           In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the…

Q: A ladder 10 meters long leans against a wall. If the bottom of the ladder is being pulled away from…

A: .

Q: If a piece of machinery depreciates continuously at an annual rate of 4%, how many years will it…

A: To find: The number of years it will take for the value of machinery to halve. Concept used: The…

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: The length of a rectangle is increasing at a rate of 5 meters per hour and the width is decreasing…

A: The length of a rectangle is 11 meters and the width is 20 meters. The length is increasing at a…

Q: For a period of time, an island's population grows at a rate proportional to its population. If the…

A: The general growth formula is given by,

Q: The population of Northern Cascadia is growing at a rate of 20% every 3 years. Assuming that it…

A: Topic: percentage

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

A:

Q: A radioactive substance has a decay rate of 4% per hour. If 1000 grams of the substance are present…

A: It is given that,a radioactive substance has a decay rate of 4% per hour. If 1000 grams of the…

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

A:

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: 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: A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are…

A:

Q: If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is the…

A: Given dr/dt = 3

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

A:

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

A:

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

A:

Q: A bunch of hooligans dump 164 pounds of  pizza boxes into a lake. If the pizza boxes dissipates at a…

A:

Q: The population of a city is 89​,000. If the population grows continuously by 3.2​% per​ year, in how…

A:

Q: If in the year 2000 there were 1.26 million metric tons of beef produced and demand is growing at a…

A:

Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

A:

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

A:

Q: Researchers recorded that a certain bacteria population declined from 100,000 to 100 in 24 hours. At…

A: We have to find number of bacteria in 8 hours into the experiment where researchers recorded that a…

Q: If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A:

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

A:

Q: The population of an endangered species decreases at a rate of 7% per year. Approximately how long…

A: Answer

Q: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

A:

Q: Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square…

A: If the area of a square, A, is x2 units , then the length of its side is x unit .

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

A:

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

A:

Q: A life raft, set adrift from a sinking ship 150 miles offshore, travels directly toward a Coast…

A: Time , distance and speed is related using a formula time=distancespeed .At the same time , both the…

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A: Given- Half life t12 =3.3 hours, Intial weight=1 gm. To find- The time in which the radioactive…

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.