At the start of 2010, an online social group had 360 million members. Subsequently, new members joined at a rate of roughly m(t)=-9.9t^2+12t+260 million members per year (0

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: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A: half life problem

Q: if the population of Palestine is 6 million in 2020  with a growth rate of 3%/yr when it is expected…

A: Given: The population of Palestine is 6 million in 2020  with a growth rate of 3%/yr

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: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A:

Q: The number of zebras in a certain area of ​​Africa grows with a speed proportional to the cubic root…

A:

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

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

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

A:

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

A:

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

A:

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: 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 company is considering expanding their production capabilities with a new machine that costs…

A:

Q: 3. The population of a community is known to increase at a rate proportional to the number of people…

A: Let initial population P0Population at time t is P.

Q: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: The city of San Estaban had a population of 45,000 in 2015 (t=0) and was growing continuously at an…

A: Initial population =45000 Growth Rate=3%=0.03 At 2016, t=2016-2015=1 So the population in 2016 is:

Q: The current circulation of some magazine is 3000 copies per week. The managing editor of this…

A:

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: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

A: Given population of world in 2015  was 9.75 billionlet   for t=0 , we have year 2015

Q: A radioactive substance decays at a rate proportional to the amount present ( y(t) = yoe-rt ) If 40%…

A: let the amount of radioactive material be x, and Given that…

Q: A bank pays interest continuously at the rate of 6%. How long does it take for a deposit of Q0 to…

A:

Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

Q: nown to grow at a rate proportional

A:

Q: Interest is compounded continuously at 5%.  How long until a $5000 investment grows to $12000?

A: Interest is compounded continuously at 5% $5000 investment grows to $12000

Q: A population of 200 rodents is growing at a rate of 5% per month. What equation model can represent…

A: The exponential growth or decay is modelled using the equation, f(t)=a(1±r)t, where a is the initial…

Q: The population of a certain bacteria culture was 40,876 after 18 hours had elapsed. After another 20…

A: Given that, The population of a certain bacteria culture was 40,876 after 18 hours had elapsed.…

Q: Find the amount after 3 years if $ 1000 is invested at an intrest rate of 12% per year, compounded…

A: Given :             The amount invested is $1000.             Interest rate = 12% per year.…

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

A:

Q: city of half a million, there are initially 400 cases of a particularly virulent strain of flu. The…

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 population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

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

Q: projected that, t months from now, the population of a certain town will be growing at the rate of…

A:

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

A:

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches per…

A:

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

A:

Q: An initial investment of $6000 grows at 5% per year. What function represents the value of the…

A: Given that initial investment made = $6000 It is said that the investment grows 5% per year. This is…

Q: A bacteria grows proportional to the square root of its current population. Starting at an initial…

A:

Q: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree…

A:

Q: If a village has a population of 2000 and a natural growth rate of 3.7% but has a carrying capacity…

A:

Q: 2. How long will it take you to get ten times your money at 2% interest compounded continuously.

A:

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…

A:

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

A: Answer

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A:

Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A:

Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A:

Q: A certain bacteria culture is observed to double its amount after two hours it was initially…

A: Let say population is P. So population at time 't' is given by P(t). Assume initial population is P0…

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.