A certain bacteria culture is observed to double its amount after two hours it was initially observed. Predict the factor the initially observed population will be multiplied to after another two hours, if the rate of growth of the culture is proportional to the current amount.

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

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

Q: A student is 25 years old and the world has a population of 6.2 billion. Assuming that the…

A: Given,  Student's current age = 25 Student's future age = 68 Time (t) = 68 - 25  = 43 Annual growth…

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: Given, the population of a certain country has grown at a rate proportionalto the number of people…

Q: After 2 hours, the population of a culture of bacteria has increased by 50%. If the rate of growth…

A:

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

A: Let's find.

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

A: Follow the steps.

Q: Suppose that during the first year after its hatching, the weight of a duck increases at a rate…

A: Solution

Q: A student is 19 years old and the world has a population of 6.6 billion. Assuming that the…

A: Given Present population (P) = 6.6 Rate (R) = 0.6% Time  (n) = 72-19= 53

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

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

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Q: After 2250 years, 25% of a radioactive material remains. If the rate of decay of the material is…

A: Half-life = 0.693/Decay constant(lambda)

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

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: In a liquid culture, the number of bacteria grows at a proportional rate depending on the number of…

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

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Q: Suppose an unknown radioactive substance produces 22400 counts per minute on a Geiger counter at a…

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

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Q: In a city with 500,000 population, the rate of the spread of a new flu epidemic is proportional to…

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: 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: A certain type of bacteria is known to grow at the rate proportional to square root of the amount…

A: To find- how much bacteria is there after 7 hours.

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: The rate of decomposition of radioactive radium is proportional to the amount present at any time.…

A: The rate of decomposition is proportional to y, we know that y=Cekt, where t is the time in years.…

Q: In a certain bacteria culture the rate of increase in a number of bacteria is proportional to the…

A: Follow the steps below to solve a differential equation(in terms of x and y) by the variable…

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

A:

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

A:

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 colony of bacteria with originally 100 cells has now grown to 900 in 2 hours. Assuming the rate of…

A:

Q: A group of survivors on a supply run has returned to their base camp with a population of 2000. Two…

A: Given:  y       = present number of infected people 2000 = total population  y'(t)  = rate of spread…

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: 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: In March 1976 the world population reached 4 billion. At that time, a popular news magazine…

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

A: Answer

Q: A scientist discovered a new material that expands at an extremely fast rate. After studying…

A: We have to use exponential growth function to solve the problem

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

A:

Q: After an hour, the population of bacteria with a number of P0 found that their number became 3 /…

A:

Q: Suppose an unknown radioactive substance produces 6400 counts per minute on a Geiger counter at 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: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A:

Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

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

A:

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…

Q: The homicide rate decreases at a rate of 3%/yr in a city that had 800 homicides/yr in 2018. At this…

A: dH / dt = rate of change of homicide rate = - 3% = - 0.03 x HPlease see the white board for…

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.