A bacteria culture starts with 140 bacteria and grows at a rate proportional to its size. After 3 hours there will be 420 bacteria. (a) Express the population P after t hours as a function of t. Be sure to keep at least 4 significant figures on the growth rate. P(t)= (b) What will be the population after 7 hours? bacteria (c) How long will it take for the population to reach 2950? Give your answer accurate to at least 2 decimal places. hours

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: a: it doubles in every 30 minute and initial population = 10 then we can write the function as:…

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A:

Q: A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present.…

A:

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

A:

Q: 6. The population of a community is known to increase at a rate proportional to the number of people…

A: We have to find the time it takes for the population to quadraple.

Q: The Loth Cat population grows at a constant relative growth rate. If the population is 400 after 2…

A: Let the constant relative growth rate be 'r' and the time in years be 't'. Let the population at any…

Q: Initially 50 grams of radioactive substance was present. After 6 hours the mass had decreased by 9%.…

A:

Q: The differential equation modeling population growth while incorporating the carrying capacity is =…

A: Given: Growth rate is 0.1 per year. Environmental limitation is of 4600 deer. Currently there are…

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: (a) Given: The initial population is 500. The number of cells in a culture doubles approximately…

Q: The air in a room with volume 180 m3 contains 0.15% carbondioxide initially. Fresher air with only…

A:

Q: 6. The number of tree frogs on an island is growing at a rate proportional to the population. The…

A: topic - exponential function

Q: The rate growth of a population is proportional to the present population. If it is 1000 initially…

A: This question is related to the population growth, We will solve it using integration.

Q: The half-life of a certain radioactive substance is 5 days. There are 28.4 g present initially. a.)…

A:

Q: 1. The population of a community is known to increase at a rate proportional to the number of people…

A: Topic:- exponential function

Q: Consider the following situation. A tank contains 2500 L of pure water, with 15 kg of salt dissolved…

A: Let consider that function s(t) is kgs of salt in the tank at time t minutesAs we know thats'(t)=The…

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

A:

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 city grows at a rate directly proportional to its population. The initial pop. is 30 and it…

A: The rate of change of the variable (Population here) is proportion to the variable itself. Hence,…

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

A:

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

A: Given that: Rate of increase of population is proportional to the number of people in the country.At…

Q: The growth rate of the bacterium, a common bacterium found in the human intestine, is proportional…

A: From the problem, we know that -The growth rate of the bacterium found in the human intestine is…

Q: A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present.…

A: We are given that: The radioactive element decays at rate 5% annually and there are 40 g substance…

Q: A wolf population is growing at a rate of 9.3% per year. Find the time at which the wolf population…

A:

Q: A bacteria colony grows at a rate of 11% per year. If the initial sample has a mass of 500 grams,…

A: We are given that the grow after each year is 11%, that means if the initial value is x, then the…

Q: A continuous income stream has an annual rate of flow at time t given: f(t)=9000e^(0.12t)…

A:

Q: 5. The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: One model for the way diseases die out when properly treated assumes that the rate dy/dt at which…

A:

Q: Radium decomposes at a rate proportional to the amount present. If the half-life is 1600 years, find…

A: NOTE: Refresh your page if you can't see any equations. . the initial amount is a=100% half-life is…

Q: If an amount P0 is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A:

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

A: We have to find the differential equation for the population growth.

Q: The half-life of radium-226 is 1590 years. (a) If a sample has a mass of 150 mg, find a function…

A:

Q: (a) A kitchen sink has a volume of 15 L. If the drain is closed and the sink is initially empty,…

A:

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A: Question- If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded…

Q: A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present.…

A:

Q: the number of bacteria in a certain population increases to a continuous exponential growth rate,…

A: NOTE: Refresh your page if you can't see any equations. . the given growth rate is  r=6.2%=0.062

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: Given The number of cells doubles every 30 minutes. A) Initial Population =1000 B) Initial…

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

A:

Q: A breeder reactor converts relatively stable Uranium 238 into the isotope Plutonium 239. After 15…

A:

Q: 15. Suppose that an amount Po, in dollars, is invested with interest compounded continuously at 4.5%…

A:

Q: In Example 2, we modeled the population size (in millions) of the United States as N(t) = 8.3(1.33)'…

A: The solution of above question no. #30 is written below with graph.

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: 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: 3. In a certain culture, the rate of growth of bacteria is proportional to the amount present. If…

A:

Q: A culture initially has N0 number of bacteria. At time t = 1 hour the number of bacteria is measured…

A:

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A: Given that if an amount P0 is invested in the Mandelbrot Bond Fund and interest is compounded…

Q: The population of Normal, Illinois grows proportionally to its population at time t. At an initial…

A: Given, dPdt=kP Where P is the population and k is the proportionality constant.

Q: A lake is initially stocked with 400 fish and in the first year the population tripled in size. a)…

A:

Q: A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They…

A: Given that initial number of fish is 100 and rate of increase of population of fish is directly…

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

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.