I) How many babies in total were born during this time period (I.e the first ten years after the 2010 population census? 2)Find time To such that the total number of babies born from the 2010 census up to To was precisely 14 thousand.

Q: The number N of bacteria in a culture is given by the model N = 175ekt, where t is the time in…

A: Given: The number N of bacteria in a culture is given by the model N = 175ekt, where t is the time…

Q: In a simple electric circuit, Ohm's law states that V IR, where V is the voltage in volts, I is the…

A: From the given problem: dVdt=-0.01 volts per second ; dRdt=0.03 ohms per secondR=300 ohms ; I=0.04…

Q: The volume of fluid in an IV (intravenous) drop decreases according to the mathematical model…

A: The  given model of the volume of fluid in IV drop versus time is:   V=-0.110t+1   Where, V is the…

Q: It is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in…

A:

Q: A manufacturer estimates that she can sell a maximum of 105 thousand cell phones in a city. By…

A:

Q: 4. The area of a semicircle is given by A = 0.5r, where r is the radius in inches. The semicircle,…

A: We need to find rate of change.

Q: At what rate in cubic centimeters per minute is the volume increasing at this instant?

A:

Q: A population of mosquitoes increases at a daily rate of 1/2 times the current population. You can…

A: Given that A population of mosquitoes increases at a daily rate of 1/2 times the current population.…

Q: a)How quickly is the water leaving the barrel over the first two seconds? b)Will the water drain…

A: The solution is given below in the next step:

Q: Suppose the Marginal product of labor in the economy is given by MPN= .002(16,000-N), while the…

A: a. The market-clearing wage rate equates the demand and supply of labour Solve for w first Therefore…

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

A: Rate of oil production is, D(t) = 3.8e0.04t billions of barrels per year where t is the number of…

Q: The population of a bacteria culture grows at a rate of P = 100(2)n, where P is the population and n…

A:

Q: In a particularly small region in the Philippines, the consumer price index C depends on • E, the…

A: Given that, The consumer price index C, which depend on The current value of the gross Domestic…

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: The city state of Tobagon island consumes gas at the rate of (2.5t +10)1/2 million barrels per year…

A: For a function: y=f(t), the dependent variable is y and the independent variable is t. The value of…

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

A: Rate of change is nothing but the change happen in any observations over a period of time. Here…

Q: Tank A initially holds 100 gallons of brine that contains 150 pounds af salt, and tank B holds 100…

A: Tank A initially holds 100 gallons of brine that contains 150 pounds of salt.Tank B holds 100…

Q: 4. A well-circulated pond contains 1 million L of water that contains a pollutant at a concentration…

A: circulated pound contains 1 million litre of water that contain important at the separation of 0.01…

Q: 3. The population of a community is known to increase at a rate proportional to the number of people…

A: Let initial population P0Population at time t is P.

Q: e) What are the domain and the range for this situation?

A:

Q: Suppose that I years from now, one investment plan will be generating profit at the rate of P1'(t)=…

A: Given. P1'(t) = 90e0.1t (1000$) P2'(t) = 140e0.07t (1000$)

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: 4. In a culture of yeast, the amount of active ferment grows at a rate proportional to the amount…

A: Let's work on the problem straight from the statement "the amount doubles in 1 hour": let the…

Q: The number of bacteria growing in an incubation culture increases with time according to n(t) =…

A: The number of bacteria growing in an incubator culture increases with time according to the function…

Q: The amount of a radioactive isotope present at time t is given by A(t)=300e−0.0283t ​grams, where t…

A:

Q: Suppose that a person learns y items in x hours, as given by y = 40/x, 0sxs 4. Find the rate of…

A: The given function is y=40x,   0≤x≤4. Obtain the derivative as follows.…

Q: 4. The growth rate of a colony of ants is given by the formula 10t 2 (1+t²)² where t is measured in…

A: The growth rate of a colony of ants is given by 10t/(1+t2)2 Initially there are 100 ants ∴ Number of…

Q: When it comes to bacteria growing by binary fission, its generation time will be the time interval…

A: Given,              G=t3.3 logbB; G= generation time  t=  time interval in hours or minutes b=…

Q: At time t years, an industry consumes fuel at the rate of (3t + 27)/³ million barrels per year. (i)…

A: Given rate of consumption of fuel = (3t + 27)^1/3 million barrels per year. (i) In the next 10…

Q: The total cost in pesos of producing x pools of low voltage cable is given by C = 0.002 x - 05 x2 50…

A:

Q: A population of insects increases at a rate of 75 + 5t + 0.2t^2 insects per day. If there are…

A: We have given that population of insects increases at a rate of 75+5t+0.2t2 insects per day.…

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

A: Pressure and Volume are related by equation At a instant

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: We need to find amount after one hour.

Q: 2. The population of the earth was 3 billion in 1970 and was increasing at a rate of 2% per year.…

A:

Q: A manufacturer estimates that she can sell a maximum of 30 thousand cell phones in a city. By…

A:

Q: 2. The liquid base of an ice cream has an initial temperature of 210°F before it is placed in a…

A: Given : The liquid base of an ice cream has an initial temperature of    To find at what time will…

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

A:

Q: With a half life of 36 hours. Suppose a patient receives a  medication of 90 milligrams at midnight.…

A: A=A0e-ktAt t=36,A=A02A02=A0e-36kk=ln236A=A0e-ln236tA0=90At noon on first day…

Q: Estimate the value of E1 (1/n²) value. to within 0.01 of its exact

A:

Q: 2. It takes a car salesman 2.5 hours to drive from one city to another if he drives at a constant…

A: We know that , distance = velocity×Time

Q: b. A spherical metal ball with initial temperature of 190°C is placed outside where the temperature…

A:

Q: Suppose a person with x years of eduction before seeking regular employment can expect to receive an…

A:

Q: A tank containing chocolate milk initially contains a mixture of 460 gallons of milk and 40 gallons…

A: Let yt be the amount of chocolate syrup in the tank at time t.  The rate of change of the amount of…

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: After a foreign substance is introduced into the blood, the rate at which antibodies are made is…

A: Please see the below picture for detailed solution.

Q: 1. There are 64.000 subscribers to an online fashion magazine. Due to competition from a new…

A:

Q: Find the number of units x that produces the minimum average cost per unit  C  in the given…

A: It is minimum average cost per unit problem.

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

A: In mathematics, two varying quantities are said to be in a relation of proportionality,…

Q: The amount of decay of a certain radioactive element is given by -0.04t Yoe' where t equals time in…

A: The amount of decay of the radioactive element is given as follows. y=y0e-0.04t where t is the time…

Q: The population of a certain bacteria culture was 49,271 after 15 hours had elapsed. After another 22…

A: Given that the population of a certain bacteria culture was 49,271 after 15 hours had elapsed.After…

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.