A culture of bacteria in a particular dish has an initial population of 200 cells grows at a rate of N'(1) = 60 e 0.21972t cells/day. a. Find the population N(t) at any time t20. b. What is the population after 14 days?

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Q: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2…

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Q: Suppose the population of a colony of ants grows at the rate P'(t) = 1 +   5 /(√ t + 1)   If…

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Q: Alice measures a radioactive sample at 1400 counts/minute on a Geiger counter. If the radioactive…

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Q: A culture initially has P number of bacteria. At t = 3hour the number of bacteria is measured to be…

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Q: A population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day (t in days). Find…

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Q: A sample of 800 g of an isotope decays to another isotope according to the function A(t)= 800 e…

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Q: dy 2. When does the differential equation Cekt represent exponential growth? exponential dt decay?

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Q: The population of mosquitoes of a colony at a rate proportional to the population present at time t.…

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Q: A sample of 400 g of radioactive lead-210 decays to polonium-210 according to the function A(t) =…

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Q: 1. A honeybee population starts with 100 bees and increases at a rate of f'(t) bees per week. What…

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Q: It is estimated that t years from now the population of a certain lakeside community will be…

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Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: 8. Let n(t) represents the rate of growth of a population of grizzly bears at time t (in years).…

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Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

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Q: If the instantaneous growth rate of COVID19 is modeled by (limHh->0)(200t+100h). At t=5 seconds…

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Q: You are a process control engineer in a water purification plant. In a certain subprocess, water…

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Q: A forester finds that a certain type of forest tree grows in such a way that its height h(t) after t…

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Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find in terms…

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Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

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Q: A sample of 500 g of radioactive​ lead-210 decays to​ polonium-210 according to the function…

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Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

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Q: A 13-g sample of radioactive iodine decays in such a way that the mass remaining after t days is…

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Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

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Q: For small, slowly falling objects, the assumption made in the text that the drag force is…

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Q: The rate of change dP of the number of wolves on an island is modeled by the following differential…

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Q: The velocity dx/dt of a chemical reaction is proportional to (a-x), where x is the amount…

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Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: A 5.40 mol sample of solid A was placed in a sealed 1.00 L container and allowed to decompose into…

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Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: Here is the Answer and Explanation

Q: Suppose for a life aged 40, we know 1–t40+t = 0.01 · (1 – t), te [0, 1]. t e [0, 1]. Calculate

A: Given: q40+t1-t=0.01×1-t        t∈0,1

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

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Q: The mass of a radioactive sample is given by M(t)=M010^-kt where t is the time in years, M0 is the…

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Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

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Q: Blood carries a drug into an organ at a rate of 3 cm3/sec and leaves at the same rate. The organ has…

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Q: A deposit of $2000 at 2% interest compound continously will grow to v(t)= 2000e0.02t dollars after t…

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Q: A radioactive element decays according to the function Q= Qn e", where Q, is the amount of the…

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Q: If oil leaks from a tank at a rate of  r(t) gallons per minute attime t , what does ∫0120 r(t) dt…

A: Oil leaks from a tank at a rate of  r(t) gallons per minute at time t.

Q: A radioactive matierial decays according to the function A0e-0.0244t where A0 is the intial amount…

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Q: During surgery a patient receives midazolam, a sedative, to produce amnesia and ensure they do not…

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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.