A model for the population P(t) in a suburb of a large city is given by the initial-value problem dP = P(10-1 - 10-7P), dt P(0) = 7000, where t is measured in months. Find the population P of the suburb at time t. P(t) = What is the limiting value of the population? At what time will the population be equal to one-half of this limiting value? (Round your answer to one decimal place.) months

Q: Assume that it costs a company approximately C(x) = 529,000 + 160x + 0.001x2 dollars to manufacture…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Suppose a population of P(t) satisfies dp/dt = 0.4P -0.001P 2 P(0) = 50 A. What is the carrying…

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Q: A model for a certain population P(t) is given by the initial value problem dP dt  =  P(10−2 − 10−12…

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Q: Consider the graph of H(t) = k(1 - 6t) where k is a positive constant. (a) Find the coordinates of…

A: (a). Horizontal intercept : (61​,0)  (b). Vertical intercept : (0,k)   Explanation:

Q: 1. The logistic equation is a classical model of population growth and is given by dx(1) = x(1) (1 –…

A: Given the logistic equation .We will first plot the function f(x).This is a quadratic function whose…

Q: where p(t) is the proportion of the population that knows the rumor at time t and a and k are…

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Q: A population of animals is growing at a rate of 7% per year and the growth can be modelled by the…

A: It is given that population of animals is growing at a rate, r = 7%= 0.07 ( decimal).  The growth…

Q: 7. Supply of a product increases according to the model S(p) = a In(p – b) thousand units per week…

A: Step:-1 Given that S(p)=a ln(p-b) thousands units per week ; Here, p denotes dollars per unit then…

Q: levels of income per capita, assuming that a = 1/3. 6. Consider the Solow model with population…

A: We have solow model

Q: model for the population P(t) in a suburb of a large city is given by the initial-value problem dP…

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Q: The biomass B(t) of a fish population is the total Suppose that at time t = 4 weeks the population…

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Q: The average pollen count in a city on day x of the pollen season is P(x) = 8x−0.2x2 (for 0 < x <…

A: Here, we are going to solve only one question and for the remaining question post the question…

Q: Suppose a population of size N is exposed to a contagious disease. If t is the time in days and y is…

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Q: A model for a certain population P(t) is given by the initial value problem dP = P(10-5 - 10-12 P),…

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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.