An object with initial temperature 150∘F is submerged in large tank of water whose temperature is 60∘F. Find a formula for F(t), the temperature of the object after t minutes, if the cooling constant is k=1.4

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

A: find explanation below

Q: A certain species of fish is to be introduced into a lake, and wildlife experts estimate the…

A: Given equation is P(t)=692(2)t3 Given population is 2768 fish To find the time t, we plug in 2768…

Q: A toxin introduces into a colony of bacteria, and t hours later, the population of bacteria is given…

A: Given:  N(t)=(5t+9)e-0.1t. As nothing is specified, we will do it by graphical method. Let us plot…

Q: A certain species of alligators is to be introduced into a swamp, and wildlife experts estimate the…

A: Given that

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

A:

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

A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

Q: The amount A (in g) remaining of a radioactive substance after time t (in years) is found by solving…

A: We have to solve the differential equation as a function of t.

Q: : Suppose that the temperature of a cup of coffee t minutes after it is poured is given by 1 T(t) =…

A:

Q: A 2,662-liter cistern is empty when water begins flowing into it (at t = 0) at a rate (in L/min)…

A: We have to find the function that gives amount of water in tank at time t.

Q: Suppose a certain drug is administered to a patient, with the percent of a concentration of the drug…

A: Given that percent of a concentration of the drug is kt=5tt2+1 Differentiate kt=5tt2+1 with respect…

Q: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

A: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

Q: A certain species of alligators is to be introduced into a swamp, and wildlife experts estimate the…

A: A certain species of alligators is to be introduced into a swamp, and wildlife experts estimatethe…

Q: In a survey, the population growth in an area can be predicted according to the equation…

A: Given: α0=30000d=4%

Q: The doubling period of a bacterial population is 10 minutes. At time t = 120 minutes, the bacterial…

A: Given:The doubling period of a bacterial population is 10 minutesAt t=120 minutes , bacterial…

Q: Suppose the height of a spacecraft at time 1 is given by f () = 27 E1 for 0 <15 3. Find an…

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

A:

Q: it is known from experiments that the height (in meter) of a certain plant after t months is given…

A: Given: ht=t-t; 0≤t≤1 for finding given values, first we draw graph of given function on given…

Q: if the population of the lunar station at clavius is given by P=200 + 30t, where t is time in years…

A:

Q: Suppose that a population of bacteria grows at a rate that slows down with time, so that the growth…

A: P'(t) is known. We have to integrate the same to obtain P(t).

Q: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

A:

Q: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

A:

Q: A certain radioactive substance decays according to the formula q(t) = q0e −0.0031t where q0 is the…

A: The radioactive substace decay equation is given byq(t)=q0e-0.0031t.........(1)where q0is the…

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

A:

Q: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the…

A: It is given that A certain species of deer is to be introduced into a forest, and wildlife experts…

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: Suppose that the concentration C of a medication in the bloodstream t hours after an injection is…

A: The concentration C of a medication in the bloodstream t hours after an injection is given by:…

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: 5. Consider the population of bacteria grows according to the function f(t) 200e0.02t, where t is…

A: The solution of the problem is given in the next steps.

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

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: For some positive constant C, a patient's temperature change, T, due to a dose, D, of a drug is…

A: As per given by the question, the patient's temperature is given by; . Now, First finding the…

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: The population of a certain inner-city area is estimated to be declining according to the model…

A: NOTE: Refresh your page if you can't see any equations. . take t=66 years

Q: past hobbits, the executive board of the oil company Denethor estimates that oil will be pumped from…

A:

Q: The population of a certain inner-city area is estimated to be declining according to the model…

A: Given: The population decline of a certain city is given as, P(t)=580000e-0.022t t- Number of years…

Q: One model for the time it will take for the world’s oil supply to be depleted is given by the…

A: One model for the time it will take for the world’s oil supply to be depleted is given by the…

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

A:

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: The amount A (in g) remaining of a radioactive substance after time t (in years) is found by solving…

A:

Q: A certain species of alligators is to be introduced into a swamp, and wildlife experts estimate the…

A: Given  Pt=931×4t2 where t is the number of years.

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: At time t=U years, a ranch has a population of 25 deer If the rate of growth of the population is…

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:

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.