The rate of investment is given by I (t) = 6 √t.

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: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Given that ,    Ecologist estimate that, when the population of a certain city is x thousand…

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

A:

Q: Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the…

A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

Q: Initially 35 grams of radioactive substance was present. After 5 hours the mass had decreased by 11…

A: Given:- Initially 35 grams of radioactive substance was present. After 5 hours the mass had…

Q: When air expands adiabatically (without gaining or losing heat), its pre and volume V are related by…

A: For decreasing rate apply negative sign

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: ologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Answer

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

A: Given that the size of the tank is 200 gallon. Half of it is full, that means 200/2=100 gallon is…

Q: After the introduction of foxes on an island, the number of rabbits on the island decreases by 4.5%…

A:

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Solve for the value

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Given, the half-life palladium-100 is 4 days. Here, we use the radioactive decay model, given as…

Q: The rate of growth of the bacterial population is proportional to the number of bacteria present at…

A: Introduction: Differential Equation applications are useful in both the classroom and in real life.…

Q: The yearly rate of consumption of natural gas (trillions of cubic feet) for a certain city is…

A:

Q: For any logistic equation, show that the point of inflection occurs at y = L/2 when the solution…

A: Given: The logistic equation

Q: A population of mites growsat a rate proportional to the number present, y. If the growthconstant is…

A: Assume population at time t is p Let f(t)=population at time t=p

Q: (For Bacteriologists). In one of your Basic Calculus sessions, a top of the class Grade- 12 student…

A: Hair we have to find out the value of Y for the different values of T

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Given :Half life of Palladium-100= 4 days

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

A:

Q: Water is pumped out of a holding tank at a rate of 7 – 7e-0.11t liters/minute, where t is in minutes…

A: NOTE: Refresh your page if you can't see any equations. . the water leaving the tank at a rate of…

Q: The population of a colony of bacteria is modeled by the function P(x) = 50(e-X -e-X* ) + 10, for 0…

A: Given that: P(x)=50(e-x-e-x2)+10

Q: Radium decomposes at a rate proportional to the amount present at any instant. If initially there…

A:

Q: Find the supply function x = f(p) that satisfies the initial conditions. dx 10 x = 140 when p = $5…

A: Here, dxdp=10p-5⇒dx=10p-5dp⇒∫dx=10∫1p-5dp+C...(1)

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: Initially there was 80 milligrams of radioactive substance present.  After an 8 hour period the mass…

A: From the differential equation from the given information. dPdt=kPdPP=kdt Here, the amount of…

Q: Suppose a tank contains 8000 gallons of oil, and this is being pumped out at a rate of 600e ,-0.05t…

A:

Q: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly heating…

A: It is given that present heating cost per month is $200. As the heating cost reduced after…

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

A: a) Revenue per user at t = 0  = $ 350  Then it decreases by 10% every year, i.e. revenue per user at…

Q: An investment pays out 800,000 Mexican pesos per year, continuously for 5 years. Find the PV of the…

A: Given, AmountA=800,000t=5 years

Q: 3. When polluted water begins to flow into an unpolluted pond, the concentration of pollutant, C, in…

A: Given that The concentration of pollutant C in the pond at t hours is modelled by

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Consider the decay of Palladium-100, The half life of Palladium-100 = 4 days and after 24 days…

Q: Several years ago, ADTF Distributors purchased a brand new cargo plane to increase their coast to…

A:

Q: The value of a computer t years after purchase is V(t) = 2, 000e-0.35t dollars. At what rate is the…

A:

Q: A culture initially has No number of bacteria. At t =1hours the number of bacteria is measured to be…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: 1.A culture has y,number of bacteria. At time t=2 hours, the number of bacteria is measured to be…

A: Given, Initial number of bacteria is y0. also, given at time t=2 hours, the number of bacteria is…

Q: A radioactive element decomposes at a rate proportional to the amount present. The amount remaining…

A:

Q: The base x of a triangle is decreasing at the rate of 5 in./sec. and the height y of the triangle is…

A: Given Base = x  Height = y Rate of change of base = dx/dt = - 5 in/s Rate of change of height =…

Q: The monthly output of a certain product isQ(x) = 2400x5/2where x is the capital investment in…

A: The monthly output of a certain product is Q(x) = 2,400x5/2, where x is the capital investment in…

Q: When air expands adiabatically (without gaining or losingheat), its pressure and volume are related…

A: Given that When air expands adiabatically (without gaining or losing heat), its pressure and volume…

Q: The size of a stray cat population at the bay area of a certain city grows at a rate of 7% monthly.…

A:

Q: A mathematical model for population growth over short intervals is given by P=P0ert​, where P0 is…

A:

Q: Assume the rate of investment is given by the function I (t) = ln t. Compute the total capital…

A: We solve this problem by using the capital formation i. e. Total capital accumulation=∫t,t2I(t)dt…

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A:

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A:

Q: The biomass of a yeast culture in an experiment is initially 29 grams. After 30 minutes the mass is…

A:

Q: Initially 47 grams of radioactive substance was present. After 10 hours the mass had decreased by…

A:

Q: The rate of investment is given by I (t) = 5vt. Calculate the capital growth between the 4th and the…

A:

Q: Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1…

A:

Q: Initially 25 grams of radioactive substance was present. After 10 hours the mass had decreased by…

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.