The number of cells in a bacteria population is given by P(t) = 1200 - 2 where t is measured in days. 1. What is the initial population of the bacteria? 2. What is the population of the bacteria after 1 days?

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Q: 5. For what values of r does the function y = e™* satisfy the differential equation 2y" + y' – y =…

A: Given , differential equation       2y" + y' - y = 0   (2D2 + D - 1)y = 0 The auxiliary equation of…

Q: A rate of change of H is given by = k(5+ H). When t = 0, H = 4. When t = 3, H dt = 10. Solve for…

A: Given :

Q: A population of insects increases at a rate of 200 + l0t + 0.25t 2 insects per day (t in days). Find…

A:

Q: The population of two different species are given by P1 P1 = 3 ln(t) +7° and P2. where t is measured…

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Q: Suppose a 1000L tank contains 400 L of fresh water at time t = 0. At that time, a salt water…

A: The solution of above question is written below.

Q: Water is drained from a swimming pool at a rate given by |(-0.2)t R(t) = 100e' gallons per hour. If…

A: Solution : We have given the rate of water drain form a swimming pool is R(t) = 100e(-0.2)t…

Q: 2. To the discrete population model for P with constant birth and death rates add a constant…

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Q: A tank originally contains 100gal of brine solution containing 20lbs of salt. At t=0, pure water is…

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Q: 1) Assume that a tumour at a rate of G(1) = 13 mg/day at time t grows %3! days. What is the total…

A: integration

Q: 29. If a factory continuously dumps pollutants into a river at the rate of tons per day, then the √t…

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Q: The number N of bacteria in a culture is given by the model N = 175ekt, where t is the time in…

A: Given: The number N of bacteria in a culture is given by the model N = 175ekt, where t is the time…

Q: A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of…

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Q: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: |The projected rate of increase in enrollment at Newhampton College is estimated |by dE 5000(t +…

A: Isolate the variables E and t in the given differential equation. dEdt=5000t+1-32dE=5000t+1-32dt

Q: Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials…

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Q: 4. The area of a semicircle is given by A = 0.5r, where r is the radius in inches. The semicircle,…

A: We need to find rate of change.

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A: The example of birthrates should follow Poisson's distribution where λi are the birthrates, since…

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Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

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

A: Given: Initial value, R0=1400 counts/min Ending value, R = 1000 counts/min Time that has passed, t =…

Q: The isotope thorium-234 has a half-life of 24.5 days. (a) What is the differential equation…

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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…

A: Given that, The population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day. At…

Q: 4. Coffee at temperature 180°F is cooling in a room with constant temperature 75°F. If it takes for…

A:

Q: for t> -1 with y(0) = 11. y =

A: First we find Integrating factor then we find solution.

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: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 4. The growth rate of a colony of ants is given by the formula 10t 2 (1+t²)² where t is measured in…

A: The growth rate of a colony of ants is given by 10t/(1+t2)2 Initially there are 100 ants ∴ Number of…

Q: |The projected rate of increase in enrollment at Newhampton College is estimated by dE 5000(t +…

A: Given, The projected rate of increase the enrollment student at Newhampton college is estimated by…

Q: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

A:

Q: Supposed that the yearly rate of consumption of oil (in millions of barrels) is given by C'(t) =…

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Q: What is the period of time ''t'' required for the initial infection rate ''I(t=0)'' to double in…

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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…

A: Given , 13gm of radioactive iodine decays in auch a way that the mass remaining after t days is…

Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: The population of two different species are given by P1 P1 = 3 ln(t) + 10 || and P2. , where t is…

A: The population of two different species are given by P1=3lnt+10 And P2=6lnt+2 Where, t measured in…

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

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Q: When sugar is dissolved in water, the amount A that re- mains undissolved after t minutes satisfies…

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Q: Suppose A is directly proportional to t. Explain what happens to t when A is increased by 5%.

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Q: Q.4 Suppose that electricity is draining from a capacitor at a rate that is proportional to the…

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Q: 8. Use a linear approximation or differentials to estimate the value of v15, knowing the exact value…

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Q: which 20 grams of salt is dissolved. Pure water is being pumped into the tank at a rate of 5…

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Q: A 50-gal barrel is filled completely with pure water. Saltwater with a concentration of 0.3 Ib/ga…

A: Given, The amount of salt in the barrel at time t is given by…

Q: Suppose a rubber ball, when dropped from a given height, returns to a fraction p of that height. In…

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Q: The Reed-Frost model for the spread of an epidemic predicts that the number I of newly infected…

A: Consider the given model, I=S1-e-rx it is given that x=17, r=0.1 and S=200

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

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Q: 17 It is found that the bloodstream concentration, C (in ug/mL), can-be modeled by C(r) T2 + 11…

A: According to the our guidelines we are supposed to do only first three subparts. Kindly repost the…

Q: Consider an animal population P(t) with constant death rate 8 = 0.01 (deaths per animal per month)…

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Q: Consider a poputation Piti satistying the extinction expiosion equation-ap - bP. where B= aPis the…

A: Given- Consider a population Pt satisfyinf the extinction explosion equation dPdt = aP2 - bP, where…

Q: 6. A certain radioactive material has a half-life of 100 days. If the amount of material present, x,…

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.