An oil storage tank ruptures at time t=0 and oil leaks from the tank at a rate of r(t)=100e-0.01t  liters per minute. a. Find a function for the total amount of oil that leaks out during the first t hours.  b. Determine the amount of time it will take for 5000 liters to leak out of the tank.

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A: (b)

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A:

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

A: Y(t)=Population in year tY(0)=700Y(15)=700+20%700=700+140=840

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A:

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Q: A population of 500 bacteria is introduced into a culture and grows in number according to the…

A: Given: pt=5001+4t50+t2 we know that population growing rate is given by differentiation of given…

Q: A population of bacteria is initially 3900. After 4 hours the population is 1300. If this rate of…

A:

Q: A population of insects increases at a rate of 260+6t+0.3t2 insects per day. Find the insect…

A: Rate of increase of population  of insects  dPdt = 260 + 6t + 0.3t2 per day

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A: The area under the graph of Nt from t=0 to t=12.

Q: 2. Consider a population of bacteria that grows according to the function f(t)=500e^0.05t , where t…

A:

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Given that, After an antibiotic tablet is taken, the concentration of the antibiotic in the…

Q: A colony of fruit flies grows at a rate proportional to its size. At time t = 0, approximately 20…

A: Let the population of fruit flies be modelled by function y.  The question mentions that the rate is…

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A:

Q: The rate of flow of a continuous income stream (in thousands of dollars per day) is given by f(t) =…

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Q: An epidemic is spreading at the rate of 18e0.2t new cases per day, where t is the number of days…

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Q: The function ​f(x)=0.08x+400 represents the rate of flow of money in dollars per year. Assume a…

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Q: The concentration of an antihista-mine in the bloodstream of a healthy adult is modeled by C = 12.5…

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A:

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Q: When $1000 is invested at r% interest (compounded continuously) for 10 years, the balance is f (r)…

A: Consider that $1000 is invested at r% interest compounded continuously for 10 years. Calculate the…

Q: The number of bacteria in a culture is given by the function n(t) = 935e0.3t %3D where t is measured…

A: the given equation is  compare this equation with  so here we have so the continuous growth rate…

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Given query is to find the maximum concentration of antibiotics in the blood during the first 12…

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A: It is given that   . Suppose a quantity Q changes over time at a known rate Q'. Then the net change…

Q: A mass of 200 grams of a particular radioactive substance decays according to the function m(t) =…

A: To find when does the mass reaches 50 grams

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Q: the income from an oil change service chain can be considered as flowing continuously at an annual…

A: Consider the function ft=10,000e0.02t. Since total income from t = 0 to t = 2 is represented by an…

Q: Let H(t) be the amount of raw honey at time t. During processing, the amount of raw honey present…

A: Answer is mentioned below

Q: #3 Find the instantaneous rate of change for the function f(x) = V3 – x at x = -6.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: In the manufacture of printing ink, solvents are used to suspend or dissolve the pigments that give…

A: Rt=10t5t2+4

Q: A mass of 200 grams of a particular radioactive substance decays according to the function m(t) =…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  find t when m=50…

Q: A population of insects increases at a rate of 20010t 0.25t2 insects per day 3. (t in day units).…

A: It is given that initially there are 35 insects at t = 0. So, I (0) = 35.

Q: A 8,000-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

A: Given the function for rate of water flowing is, Here t is measured in minutes. a. Given the time…

Q: A 12,000-liter cistern is empty when water begins flowing into it (at t = 0) at a rate (in L/min)…

A: Note: As per the guidelines we are supposed to answer only 3 sub parts, kindly repost the complete…

Q: Water is pumped out of a holding tank at a rate of 3-3e-0.5t liters/minute, where t is in minutes…

A:

Q: Water flows from the bottom of a storage tank at a rate of r(t) = 4(50 − t)e −0.05t liters per…

A: Given:  rt=450-te-0.05t    , 0≤t≤50    1 We need to find the amount of water that flows from the…

Q: A culture initialy has N mumber of bacteria. At t = 1 hour the mumber of bacteria is measured to be…

A: Let N be the number of bacteria at time t. The rate of increase which is proportional to N = dNdt…

Q: A 7,986-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

A:

Q: 13. Snow falls during a storm at a rate of t(4–t) inches per hour, as a function of time t in hours.…

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Q: The number of bacteria in a culture is given by the function n(t)=950e^0.35t where t is measured…

A: The number of bacteria in a culture is given by n(t) = 950e^{0.45t}e0.45t

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: To determine a function P(t) that models the number of bacteria after t minutes.

Q: Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set off to clear a road.…

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.