An object with initial temperature 150°F is submerged in large tank of water whose temperature is 70°F. Find a formula for F(t), the temperature of the object after t minutes, if the cooling constant is k = 0.2 F(t)=

Q: If an archer shoots an arrow straight upward with an initial velocity of 160ft/sec from a height of…

A: If the arrow reaches the ground then h(t)=0…

Q: The size P of a small herbivore population at time t (in years) obeys the function  P(t)e^0.28t if…

A: The size P of a small herbivore population at time t (in years) obeys the function When P(t)=4000…

Q: Because of the absence of predators, the number of rabbits on a small island increases at a rate of…

A: Given that the growth function is: y(t) = y0ekt. At, t=0, y(0) = y0 [This is the initial…

Q: From the beginning of the year 2000, the annual world demand for oil has increased. To account for…

A:

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

A: find explanation below

Q: If the rate of excrection of a bio-chemical compund is given by f ' ( t ) = 0.03 e -0.03 t , the…

A:

Q: Given a cooling coefficient y of 0.1, how long does it take water at 20°C to freeze (reach 0°C) in…

A: Newton's law of Cooling is used

Q: The projected rate of increase in enrollment in a new college is estimated by dE/dt= ( at+1)^-1(…

A: Given the projected rate of increase in enrollment in a new college is dE/dt= ( at+1)^-1( a+1). We…

Q: Suppose the quantity (in grams) of a radioactive substance present at time t isQ(t) =…

A: Radioactive substances have different rates of decomposition.

Q: The space vehicles are supplied power from nuclear energy derived from radioactive isotopes. The…

A: Let's find.

Q: Given the function f(x)=x2/3, which of the following is a valid formula for the instantaneous rate…

A:

Q: An investment earning interest at the rate of 10%, compounded continuously, will double in tyears.…

A: Let's solve,

Q: A container of hot liquid is placed in a freezer that is kept at a constant temperature of 20°F. The…

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: A cyclist rides down a long straight road at a velocity​ (in m/min) given by v(t)=100−10​t, for…

A:

Q: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate…

A: fx=x23fx+h=x+h23At x=8f8+h=8+h23f8=823=23×23=4

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

A:

Q: Suppose that the instantaneous rate of change of the untreated mosquitoes is 1204 at t=1, where t…

A: Let the population of untreated mosquitos be M(t). And, M(t) satisfies the equation dMtdt=kM, where…

Q: the number of cell phone subscribers in a certain country in the early 2000s was projected to follow…

A: We use differentiation and integrations to solve this problem.

Q: Suppose the quantity (in grams) of a radioactive substance present at time t is Q(t) = 2500 (5…

A:

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.1e0.007" , where t = 0 is…

A:

Q: One hour after a dose of x milligrams of a drug Predamestane is administered to a person, change in…

A:

Q: A population of bacteria is growing according to the equation P(t)=1350e^0.11t Estimate when the…

A: Substitute P(t)=2418 into the equation Pt=1350e0.11t and solve for t:…

Q: A population of bacteria is growing according to the equation P(t)=850e0.22tP(t)=850e0.22t. Estimate…

A:

Q: A body whose temperature is 50°F is placed in a warming oven whose temperature is 100°F. After 5…

A:

Q: The marriage rate in a certain country in 1990 was 0.95%, and there were about 351,000 marriages…

A: 1990 corresponds to t=0 So, M0= 351000 And r= 0.95% = 0.0095 So the model is:

Q: A 2000-liter cistern is empty when waterbegins flowing into it (at t = 0) at a rate (in L/min) given…

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

Q: Suppose that the rate at which the concentration of a drug in the blood changes with respect to time…

A: Given:The rate of change of concentration of a drug in blood with respect to time t is

Q: The rate of growth of a microbe population is given by m'(t) = 22t e ,2t where t is time in days.…

A: We will find the number of microbes in first two days.

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.4e0.007t When will the…

A: find the value of t when population is double from what it is when time is zero.substitute value of…

Q: a) What is the maximum amount of the salt that will ever dissolve in the methanol? b) If x = 50 when…

A:

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

A:

Q: If f'(t)=2t is a production rate, measured in items per hour, then how many items were produced from…

A:

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: The volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t =…

A: Given that the volume of sphere is increasing at a rate proportional to the reciprocal of its…

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: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

A:

Q: The number of bacteria in a culture is given by the function n(t)=960e0.4tn(t)=960e0.4t where tt is…

A: Exponential Population model

Q: The population of a city (in millions) at time tt (in years) is P(t)=2.7e0.002tP(t)=2.7e0.002t,…

A:

Q: If an object is projected upward from ground level with an initial velocity of 160ft per​ sec, then…

A: given  s(t)=−16t^2+160t

Q: The following equation represents the growth of bacteria in a particular food product, where t…

A: Given, the number of bacteria function f(t) = 700e0.1t , where t is time in days. When the bacteria…

Q: The size of P of a small herbivore population at time t (in years) obeys the function P(t) =…

A:

Q: The rate of growth of a fish population was modeled by the equation G(t) =…

A: Consider the given: Gt=90000e−0.6t1+5e−0.6t2

Q: The population of a city (in millions) at time t (in years) is P(t)=2.8e0.008t, where t=0 is the…

A: Given data:   The expression for the given population at any time t is: P(t)=2.8e0.008t.     The…

Q: The rate of change of the population of a certain town is given by R(t) = 50e0.05t, where t is the…

A: The rate of change of the population of a certain town is given by R(t) = 50e0.05t, where t is the…

Q: A pitcher of buttermilk initially at 27°C is to be cooled by settling in on a place where the…

A: At time t=0 minutes, temperature of buttermilk = 270C   At time t=20 minutes, temperature of…

Q: A stone is thrown vertically into the air at an initial velocity of 71 ft/s. On a different planet,…

A:

Q: If the rate of excretion of a bio-chemical compound is given by f()= 0.01 e0.011 the total amount…

A:

Q: A bacteria has a reproduction rate of r(t) = t/t^2+1 in millions of bacteria per hour, where t is in…

A:

Q: It is known from past experiments that the height (in feet) of a given plant after t months is given…

A:

Q: if the rate of growth of the population of deer in a forest is modeled by R(t)= 2000e^(0.23t) deer…

A: The rate of growth of the population of deer in a forest is modeled by R(t)= 2000e(0.23t) deer per…

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.