5. Cloudy with a Chance of Calculus In the town of Swallow Falls, Flint Lockwood has...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
5. Cloudy with a Chance of Calculus In the town of Swallow Falls, Flint Lockwood has made a startling breakthrough. His new invention, the FLDSMDFR, is producing an almost endless supply of food. The rate of food production (megatons of food/month) can be modeled by the following differential equation: F' (t) = 0.5t +2t+5 e a. (6 pts) Flint is trying to figure out the total amount of food being produced over the next two months (from t = 0 to t = 2 months) to see if the town will be buried. Using a Riemann sum, approximate this value. Use a step size of At 0.5. On the graph of F'(t) below, show what you've calculated with this sum. 5- F'(t) 01 t b. (4 pts) Find the exact amount of food being produced over the next two months (t = 0 to t = 2). 80 6. Bacteriophage lambda (a virus), regulates its decision to initiate lysis in an infected cell or remain dormant (lysogeny) using a single transcription factor, Cl. As long as enough CI is present in the infected cell, lysis is repressed. But if CI levels drop below a critical level, lysis is initiated. This system can be modeled by the following differential equation, which includes both CI production and degradation: CI' = [input] - - r * CI Both production and degradation (r = 0.5) are represented in the graph below: Cl production/degradation 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 L 0 0.5 1 1.5 2 intracellular Cl 2.5 3 3.5 a. (3 pts) Draw a single phase portrait for r = 0.5 that communicates the stability of all equilibrium points. 9 b. (6 pts) Draw a bifurcation diagram using the following values of r: 0.3, 0.5, 0.8 c. (2 pts) What kind of bifurcation is represented above? lasso saddle-node pitchfork transcritical 10 5. Cloudy with a Chance of Calculus In the town of Swallow Falls, Flint Lockwood has made a startling breakthrough. His new invention, the FLDSMDFR, is producing an almost endless supply of food. The rate of food production (megatons of food/month) can be modeled by the following differential equation: F' (t) = 0.5t +2t+5 e a. (6 pts) Flint is trying to figure out the total amount of food being produced over the next two months (from t = 0 to t = 2 months) to see if the town will be buried. Using a Riemann sum, approximate this value. Use a step size of At 0.5. On the graph of F'(t) below, show what you've calculated with this sum. 5- F'(t) 01 t b. (4 pts) Find the exact amount of food being produced over the next two months (t = 0 to t = 2). 80 6. Bacteriophage lambda (a virus), regulates its decision to initiate lysis in an infected cell or remain dormant (lysogeny) using a single transcription factor, Cl. As long as enough CI is present in the infected cell, lysis is repressed. But if CI levels drop below a critical level, lysis is initiated. This system can be modeled by the following differential equation, which includes both CI production and degradation: CI' = [input] - - r * CI Both production and degradation (r = 0.5) are represented in the graph below: Cl production/degradation 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 L 0 0.5 1 1.5 2 intracellular Cl 2.5 3 3.5 a. (3 pts) Draw a single phase portrait for r = 0.5 that communicates the stability of all equilibrium points. 9 b. (6 pts) Draw a bifurcation diagram using the following values of r: 0.3, 0.5, 0.8 c. (2 pts) What kind of bifurcation is represented above? lasso saddle-node pitchfork transcritical 10
Expert Answer:
Related Book For
Posted Date:
Students also viewed these chemical engineering questions
-
Hyten Corporation On June 5, 1998, a meeting was held at Hyten Corporation, between Bill Knapp, Director of Marketing/Sales, and John Rich, director of engineering. The purpose of the meeting was to...
-
1. Hannah is applying for a life policy on her girlfriend Sarahs life. The policy is $500,000 and carries a large premium. Hannah is the main earner, so she is concerned about not being able to pay...
-
What is a safe edge on a file?
-
During PCR, which cycle of DNA replication results in a double-stranded, unit-length DNA product? How does the rate of accumulation of this product differ from that of the DNA product wherein only...
-
Nike is a global brand, yet it alters its promotions to meet local tastes. Go to store.nike.com/gb/en_gb/ and explore the U.K. site. Now go to the U.S. site. How are these websites different?
-
X rays diffract from a crystal in which the spacing between atomic planes is \(0.175 \mathrm{~nm}\). The second-order diffraction occurs at \(45.0^{\circ}\). What is the angle of the first-order...
-
The July 6, 2011, edition of the Wall Street Journal Online includes an article by Michael Rapoport entitled U.S. Firms Clash Over Accounting Rules. The article discusses why some U.S. companies...
-
You are a market risk analyst at a small bank and need to run the stress testing based on the US FRB's stress testing scenarios. Estimate P&L based on the stress scenarios provided: Q1: In the yellow...
-
Anna has sued the city of Beaver Falls in federal court for a perceived civil rights violation. Beaver Falls is savvy and makes a Rule 68 settlement offer for $10,000 with costs then accrued. Anna...
-
Henry Incorporated manufactures a high volume of identical flashlights called the Illumin-8. The company reported the following for the month of August: Physical Units Beginning work in process,...
-
Consider an infinitely repeated Cournot duopoly with discount factor = 0.9, unit costs of c = 0, and an inverse demand function p(Q) = 10 - Q. Firm 1 is more powerful than firm 2 such that in any...
-
Under what conditions can temporary residents lose their status and privilege?
-
When the general ledger is out of balance, it indicates that? Explain.
-
Estimates for the current year were as follows: Total manufacturing overhead: $300,000 Total machine hours: 3,000 Total labor hours: 6,000 Total labor cost: $120,000 The Victor's Valves (a customer!)...
-
Define and explain the importance of the concept of 'independence as it relates to auditing.
-
Given find the value of k. es 1 e kx dx = 1 4'
-
The times required by students to complete a statistics test. State whether the data described are discrete or continuous and explain why?
-
Number of cars crossing the Golden Gate Bridge each hour. State whether the data described are discrete or continuous and explain why?
-
The speeds of cars as they pass the center of the Golden Gate Bridge. State whether the data described are discrete or continuous and explain why?
Study smarter with the SolutionInn App