A model for the population P(t) in a suburb of a large city is given by theinitial-value problemdpdta.b.= 0.1 P(1C.d.P1000,000where t is measured in months.The limiting value of the population and the time will take the populationbe equal to one-half of this limiting value respectively are-), P(0) = 3000,5000,29.11000,000, 58.12500,85.11000,000 55.5

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Answered: A model for the population P(t) in a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose the Consumer Price Index. (CPI), can be modeled by the following equation between the years 2000 and 2019: CPI(1) = 200 – 10te – 100e 0
A): What is the carrying capacity of the population? B): What is the total population at the moment the population is growing at the fastest rate? Please find part A and B
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(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.
4. In the city of Calcary, temperatures tend to range from a low of –15" Celsius to a high of 30" Celsius. The number of days, in one year, that the city experiences temperatures below T degrees Celsius, is given by D(T) = 14e - 15 s Ts 30 dx -15 (a) As part of a project on reducing energy consumption due to heating you are asked to estimate the following quantity: The number of days, in one year, that the temperature in Calcary is below 0° Celsius. If you had to make sure to underestimate this quantity, which numerical integration method would you use? Justify.
The Ramos family combined annual income is 850,000 pesos last year, This Year, the said amount increased by an additional 150,000 pesos. Find the ratio of Ramos Family's combined annual income for this year compared last year.
number of people who will be infected by t = 12 days. 7. Assume we are considering the survival of whales and that if the number of whales falls below a minimum survival level m, the species will become extinct. Assume also that the population is limited by the carrying capacity M of the environment. That is, if the whale population is above M, then it will experience a decline because the environment cannot sustain that high a population level. a. Discuss the following model for the whale population dP dt = k(MP)(Pm) where P (t) denotes the whale population at time t and k is a positive constant. b. Graph dP/dt versus P and P versus t. Consider the cases in which the initial population P(0) = Po satisfies Po

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