The difference equation for the growth of circular colonies of bacteria is Nt+1 Nt + RK N. This equation was based on the idea that nutrients for growth are available only atthe colony-environment interface. The continous-time version is presented below, where k is a positive constant and n is the number of bacteria. Solve the differential equation tofind the size of the colony as a function of time. (Let n(0) no. Assume that the population grows.)n(t) =dndt= kn¹/2=

Answered: The difference equation for the growth…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Suppose a certain country's population has constant relative birth and death rates of 97 births per thousand people per year and 47 deaths per thousand people per year respectively. Assume also that approximately 30,000 people emigrate (leave) from the country every year. Which equation best models the population P = P(t) of the country, where t is in years? dP A. dt = 50P + 30000 dP B. at C. D. **** dP at dP 0.05P - 30000 = 0.05P+ 30000 dt = 0.5P 30000 dp E. dt = 0.5P - 30
According to Newton's Law of Cooling, the temperature T of an (as a function of time t) is given by T(t) = T, + D,e, where k is a positive constant, and D, is the difference between T(0) (the temperature at time t = 0) and T, (the temperature of the surroundings). If a bowl of soup with temperature 210 degrees Fahrenheit is set down in a room with temperature 65 degrees, after how many minutes will the soup's temperature reach 100 degrees? = 0.05] 10. [for this soup, assume k
At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (r) hours was proportional to the volume (V) of the tank. This means that AP =-kV . dt Show that V= Ve is a solution of this equation. Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (iii) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?
Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation =k(TA), where T is the temperature of the object after t units of time have passed, A is dT dt the ambient temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 62 degrees for 14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees? Include at least 2 decimal places in your answer. minutes
On a monthly basis, when a factory employs L worker-hours of labor, they can produce Q(L) = 7L + 40L/6 scooters. An investment in labor of K dollars gives them an employment level of L(K)=0.055K – 12,500 K worker-hours. The factory currently invests 2,000 dollars in labor. At what rate is the number of scooters being produced changing with respect to the amount they invest in labor? Round your final answer to 2 decimal places and include units with your answer. а.
The average adult takes about 12 breaths per minute. As a patient inhales, the volume of air in the lung increases. As the patient exhales, the volume of air in the lung decreases. For t in seconds since start of the breathing cycle, the volume of air inhaled or exhaled since t = 0 is given,' in hundreds of cubic centimeters, by 2n A(t) = - 2cos 5 + 2. (a) How long is one breathing cycle? i seconds (b) Find A' (3) and explain what it means. Round your answer to three decimal places. A' (3) = i hundred cubic centimeters/second.
Based on data from 1997-2005, the amount of yogurt produced in the UnitedStates annually may be modeled byy(t) = 14.99t2 + 62.14t + 1555 million poundswhere t is the number of years since 1997.(a) Find and interpret the meaning of y(12).(b) Find and interpret the meaning of y'(12).

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