Question

RIVERDALE You find a letter from the Black Hood to the town of Riverdale "This is the Black Hood. I am the man who shot the adulterer at Pop's. I killed the child predator in Greendale. I shot the drug and sex addicted teenagers at Lovers' Lane. Riverdale is not innocent. It's a town of hypocrites, degenerates and criminals. My wrath is the price of your lies, your secrets, your sins. I will not stop. I am the wolf. You are the flock. This is the bloodletting. You will hear from me again. Due to the Black Hood running widespread in Riverdale, many of the town folks are moving out. The population of Riverdale is decreasing at a continuous rate of 0.5% per month. The Black Hood has been killing Riverdale's population by 13 people per month. NOTE: For graph scaling, it might be best to change your scale in hundreds, for example 3400 becomes 34 (in hundreds). However, all your final answers, put in the correct format, meaning don't write 34, write 3400. Write a differential equation that models how the Black Hood is killing Riverdale's population (Hint: 1. Let 13 equal his kill rate and thus will be the rate in and rate out is the decreasing population) 2. Suppose initially in the population of Riverdale is 3400 people. What is the rate the Black Hood is killing the population at the beginning of the first month? 3. Write the general solution for your differential equation in part 1. Find the particular solution based on the information in part 2. Graph your solution. Based on part 4, what would you expect the population to be at the end of 12 months? Round to the nearest person. At the rate the Black Hood is killing the Riverdale population, will the population eventually die out? Prove why/why not? Graphs are NOT proof. Hint: Use your solution from part 3. Betty and Jughead have decided when the town population gets to 2700 people they are going to leave. When will this occur? Round to the nearest month and then convert to years. What is the equilibrium value of your differential equation and what does it mean in terms of the Black Hood's kill rate and the population? Graph three functions 1) your particular solution from part 4 above 2) the equilibrium solution and 3) if the initial population was 2700 (instead of 3400). Explain what is happening with all three of these graphs. 4. 5. 6. 7. 8. NOTE: This project may take defining key terms in the problem before leading into the results to ensure your classmates understand the procedure being presented.

number 8??

Answer 1

ime S g.1 lef k killing of no.People t tiime înmomtes e or killi olt ol t dlt olt Slaclk Hoodl auズ . 00冠 akto oit as inutfallv m*O m=0 ts olt 115 dk → Rate of killiv, initially A1 nift Partical solutiom k 13t-13 R13)

20 10 10 -10 10 20