The time rate of change of a rabbit population P is proportional to the square root of P. At time t = 0 (months) the population numbers 100 rabbits and is increasing at the rate of 20 rabbits per month. How many rabbits will therebe one year later?

Q: The time rate of change of an alligator population P in a swamp is proportional to the square of P.…

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Q: Q1. In a study of Bacterial Growth, it is assumed that, a culture initially has Po number of…

A: P0 → initially number of bacteria.at t= 2h, number of bacteria→52P0We can model the problem as :P(t)…

Q: In Germany the rate of change of a population with respect to time (in years) is proportional to the…

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

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Q: If l represents the intensity of light which has penetrated water to a depth of x feet, then the…

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

A: Assuming continuous compounding P=P0eKt P→Population at moment in time P0→initial Population…

Q: In a certain culture of bacteria the rate of increase is proportional to the number present. a. If…

A: Explained below

Q: The value of a computer t years after purchase is v(t) = 3000 e -0.35t At what rate is the…

A: Please see the answer in step 2

Q: The rate of change of a certain population P at time t is modelled by the equation· dt = (100 –P).…

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Q: The rate of change of a certain substance is proportional to the amount of substance is 10 grams at…

A: Given:- The rate of change of a certain substance is proportional to the amount of substance is 10…

Q: When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of…

A: Consider the approximation cost of goods. Ct=p1.05t Rate of change of C=dCdt. So, Differentiate the…

Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

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Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

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Q: The value V of a machinet years after it is purchased is inversely proportional to the square root…

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Q: A thermometer is taken from a room where the air temperature is 60 ° F, to the outside where the…

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Q: The temperature in a laboratory is maintained at 20°C. A warm bath is left to cool down and the rate…

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Q: A certain bacteria culture is observed to double its amount after 150 minutes it was initially…

A: It is given that; let current amount of population is =N The rate of growth of culture is ∝ (N)2…

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

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Q: The population of a city doubles in 50 years. How many years will it be four times as much? Assume…

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Q: Q1) The growth rate of a certain strain of bacteria is unknown, but assumed to be proportional to…

A: The exponential growth or decay is modelled using the formula: Nt=N0ekt, where N(t) is the…

Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: The rate of change of the male population of a particular barangay is proportional to the male…

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Q: 1. If the growth rate of a culture of bacteria is proportional to the number of bacteria present.…

A: Given:  If the growth rate of a culture of bacteria is proportional to the number of bacteria…

Q: e. An airplane flying on a straight flight path will be exactly above a radar tracking station,…

A: Given: Perpendicular distance between station and plane is 5,000 km.   To find rate of distance of…

Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: In a certain culture of bacteria, the rate of increase is proportional to the number present. We…

Q: In a certain bacteria culture the rate of increase in a number of bacteria is proportional to the…

A: Follow the steps below to solve a differential equation(in terms of x and y) by the variable…

Q: Let C(t) be the concentration of a drug in the bloodstream. As the body eliminates the drug, C(t)…

A: Given, C’(t) = kC(t) We have to calculate the concentration at time t also calculate the time when…

Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We will find in how many year the population of country will be five times as shown below

Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A:

Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A:

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

A: Let,Decay rate = r = -dAdt                        negative because it's decaying/decreasingwhere, r…

Q: The population of country doubles in 100 years. How many years will it be five times as much? Assume…

A: Denote T as the total population of the country, denote S as the initial population in the country…

Q: The rate of change of the number of coyotes N(t) in a population is directly proportional to 650 −…

A: Consider N(t) as the population of the coyotes after t years. Consider the given statement as the…

Q: A water tank has 142 gallons of water, At first, in t=0, a solution with 1/6 lb/gal of a chemical…

A: it is mixing problem we use linear differential equation to solve this question.

Q: The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of…

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Q: A population of bees are dying at the rate proportional to the size of the initial hive, H(t), where…

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Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

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Q: IfI represents the intensity of light which has penetrated water to a depth of x feet, then the rate…

A:

Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A:

Q: The population of Barangay Siksikan is increasing at a rate of proportional to its current…

A: given: The population of Barangay Siksikan is increasing at a rate of proportional to its current…

Q: 2. The kinetic energy (E) of a moving object is directly proportional to the square of its velocity.…

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Q: At what speed should a fish swim upstream so as to reach its destination with the least expenditure…

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Q: After t seconds, the electric charge A of a circuit decays according to the formula A = A,e where Ao…

A: Given A=A0e-td Where, A0= Initial charge and d=Real constant   A0= Initial charge=10 units Charge at…

Q: A culture initially has P0 number of bacteria. At t=3 hour the number of bacteria is measured to be…

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Q: A culture initialy has N mumber of bacteria. At t = 1 hour the mumber of bacteria is measured to be…

A: Let N be the number of bacteria at time t. The rate of increase which is proportional to N = dNdt…

Q: 3. In a certain culture, the rate of growth of bacteria is proportional to the amount present. If…

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Q: (a) The rate of change of P is proportional to N. When t = 0, N = 250, and when t = 1, N = 400. What…

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Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We can find the answer as below.

Q: Q.3. The rate at which a body cools is proportional to the difference between the temperature of…

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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.