2. In a community of 10000 people, the rate at which a rumor spreads is jointly proportional to the number of people who have heard the rumor and the number of people of who have not heard it. When 20 people heard the rumor, it is being spread at the rate of 250 people per hour. Find a mathematical model expressing the rate at which the rumor is spreading as a function of the number of people who have heard it.

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

Q: In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was…

A: We need to find out the year in which the cost of mailing a first class letter reach 60 cents.

Q: Solve the following problems completely. 1. If a body whose temperature is initially 200° C is…

A: Use Newton's law of cooling

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A:

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A:

Q: The consumer price index, C, depends on the current value of gross regional domestic expenditure E,…

A: Let's find.

Q: A construction team gives an estimate of three months to repave a large stretch of a very busy road…

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Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 710…

A:

Q: The median size of a new single-family house built in the United States between 1987 and 2001 can be…

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A:

Q: An initial investment of $10,000 grows at 11% per year. What function rep R) - 10,000(1.11)' A) -…

A: Initial Investment f(0)=$10,000 rate r=11% per year  time = t

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

A:

Q: The population of a state is known to grow at a rate proportional to the number of people presently…

A: Follow the steps.

Q: Consider the constant rate of decrease of a certain microorganism. At the start, there are 10 000…

A: Let's find.

Q: A company's cost in dollars to produce n shoes is given by C(n)=5700+50n+0.75n^2. Assume that…

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

A:

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: Suppose the quantity x of Super Titan radial tires made available each week in the marketplace is…

A: Given,

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A:

Q: Suppose that the price p​ (in dollars) and the weekly sales x​ (in thousands of​ units) of a certain…

A:

Q: Consider the constant rate of decrease of a certain microorganism. At the start, there are 50000…

A: Given query is to find the population of microorganisms after 50 second.

Q: In an laboratory, a culture of N strands of bacteria is analyzed. It is found out that the rate of…

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

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Q: A population of 1000 students are in a dormitory. If initially, a virus infected 25 of them. If the…

A: Let number of students infected at time t be x  Then, number of healthy students at time t = (1000 -…

Q: A certain type of bacteria is known to grow at the rate proportional to square root of the amount…

A: To find- how much bacteria is there after 7 hours.

Q: In response to rising concerns about identity​ theft, the number of models of paper shredders a…

A: It is given that, in the year of 1993 the model was 3 and in the year of 2008 the model was 38.

Q: In 1991 it was estimated that there were about 100 breeding pairs of Northern Spotted Owls. It was…

A: Topic: population decline

Q: A businessman found out that there is a need for a great supply of a certain type of ornamental fish…

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A:

Q: The average cost function for the weekly manufacture of retro portable CD players is given by C(x) -…

A:

Q: (2) The number of women in the workforce, based on data and projections from 1950 to 2050, can be…

A:

Q: Suppose that a community contains 15,000 people who are susceptible to Michaud’s syndrome, a…

A:

Q: he population of a certain state is known to grow at a rate proportional to the number of people…

A: Given: The population of a certain state is known to grow at a rate proportional to the numberof…

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

A:

Q: The number of children in a church is increasing at a rate that is proportional to the number of…

A: We will find the number of children after 5 years as following.

Q: 6. Create a linear function equation that has a rate of change of -3 and a solution at (5,2).

A:

Q: A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of…

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Q: A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500…

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Q: (3) The demand function for a tablet is given by the model p=200–16x² where p is measured in dollars…

A: Given query is to find the number of units produced to get the same profile of 125 million dollars.

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

A: In a particular very small region, the consumer price index, C, depends on the current value of…

Q: In the theory of learning, the rate at which a subject is memorised is assumed to be proportional to…

A: The subject to be memorized is given by At at time t. The total amount of subject to be memorized is…

Q: In Example 2, we modeled the population size (in millions) of the United States as N(t) = 8.3(1.33)'…

A: The solution of above question no. #30 is written below with graph.

Q: (3) The demand function for a tablet is given by the model p 200 – 16x where p is measured in…

A:

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: Suppose an unknown radioactive substance produces 6400 counts per minute on a Geiger counter at a…

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Q: firm which produces a single product is interested in determining the functions that expresses…

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Q: Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain…

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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.