If f (3) = 5, g(3) = 2, f'(3) = 4, g'(3) = -4, and h(x) = 18. h'(3)? %3D what is 9(2). O 7 O -1 O -12 O 4 O 9

Q: The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: Given that rate of decay of radium is proportional to the amount present at that time.

Q: When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104…

A:

Q: A breeder reactor converts relatively stable uranium 238 into the isotope plu- tonium 239. After 15…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

A: we know that population growth formula A(t)=P0ekt where A(t) : population at time t P0 : initial…

Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

Q: The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a…

A:

Q: 2. The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: A(t) = amount remaining in t years          = A0ekt, where A0 is the initial amount and k is a…

Q: When time is measured in​ days, the decay constant for a particular radioactive isotope is 0.16.…

A: The equation for radioactive decay is N(t)=N0(e-λt), where N(t) is the new amount of isotope , N0is…

Q: A study of a certain Subanen community suggests thatt years from now, the average level of carbon…

A: Given query is to find the rate of change of carbon monoxide after 2 years.

Q: The rate at which radioactive nuclei decay is proportional to the number of nuclei that are present…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Given that , The radioactive material is known to decay at a rate proportional to the amount…

Q: at a rate proportional to the current population, and in the absence of other factors, the…

A: Consider at time t the population of mosquitoes is N in the area

Q: After a long study, three scientists conclude that a eucalyptus tree will grow at a rate of…

A: Given the rate of change= 0.6+4/(t+2)2 feet per year To find the total number of feet grown during…

Q: .

A: We will find the temperature.

Q: When we take measurements of the same general type, a power law of the form y = αxβ often gives an…

A:

Q: If f10,500 is invested fie 3 4ears at a rate of 9%.how much willyou have if interest Es compounded…

A: P=10500t=3 years.r=9%=0.09To find A

Q: The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can…

A:

Q: s projected that x years from now the population of a certain city will be changing at the rate of…

A:

Q: a city grows at a rate directly proportional to its population. The initial pop. is 30 and it…

A: The rate of change of the variable (Population here) is proportion to the variable itself. Hence,…

Q: 2. The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at…

A:

Q: 2.2 Consider the impact function of a certain drug, I = 0.25D/100 – D, with I a percentage and D in…

A: Use average rate formula

Q: The half-life of polonium is 139 days, but your sample will not be useful to you after 95% of the…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A:

Q: In monitoring the blood alcohol content of a person, the bloodstream, which is composed of 5L of…

A: Given: Bloodstream is composed of 5L of water The rate of single inflow, by absorption of fluids…

Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

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

A: Given : A town predicts that its public school population will decrease at the rate of

Q: 5. Consider the problem: A water bucket is being filled with water from a water faucet at a constant…

A:

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) her shadow on the…

A:

Q: A certain population of bacteria doubled after 20 minutes. If it is known that it grows proportional…

A:

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A:

Q: 1. For a certain radioactive element decays at a rate of 37.7% per day (tis measured in days). How…

A: We need to find time.

Q: Suppose a student is a carrier of the flu virus and returns to his isolated campus of 1000 students.…

A:

Q: It is estimated that t months from now, the population of a certain town will be changing at the…

A: This question is related to population growth, We will solve it using integration.

Q: In monitoring the blood alcohol content of a person, the bloodstream, which is composed of 5L of…

A: To determine the equation to determine the amount of alcohol in the body at a time.

Q: In a chemical reaction, a certain compound changes into another compound at a rate proportional to…

A: Let y be the unconverted amount of substance A at time t. Thus, the given information can be written…

Q: A certain population of bacteria grows at a rate that is proportional to the number present. It is…

A: Given that: Growth rate of bacteria ∝ Number of bacteria presentNumber doubles in 2 hr

Q: A 100L-capacity tank initially holds 80L of fresh water. A brine solution is poured into the tank at…

A: A brine solution is poured into the tank at the rate of 4 L/hr, while the well-stirred mixture…

Q: When we take measurements of the same general type, a power law of the form y = ax often gives an…

A: (b)   Given that X´=log(X) and Y´=log(Y)   X Y X´ Y´ 2 1.81 0.30103 0.257679…

Q: (4) Consider the constant rate of decrease of a certain microorganism. At the start, there are…

A: We have to find the number of microorganisms that will be there after 45 seconds.

Q: In a chemical reaction, substance A decomposes at a rate proportional to the amount of A present. It…

A: This decomposition reaction of first order, because rate is directly proportional to the…

Q: If f(x) = 5x -3 , compute the instontoneus rate of change of Sx) at x-2. OA -3/49 O8.7/41 oc-7/41…

A:

Q: A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They…

A: Given that initial number of fish is 100 and rate of increase of population of fish is directly…

Q: 4. If caffeine has a half-life of 2 hrs., how many of 140 mg of caffeine remain in Mr. Moreno's…

A:

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5V9x2 –…

A:

Q: A culture of bacteria grows at a rate that is proportional to the present number. It is found that…

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.