Answer asappp (1 point) A rumor spreads through a school. Let y(t) be the fraction of...
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.) dy (b) Solve the differential equation. Assume y(o) (c) A small town has 2100 inhabitants. At 8 AM, 100 people have heard a...
The equation N(t) = 1100 1 + 195e−0.625t models the number of people in a school who have heard a rumor after t days. To the nearest tenth, how many days will it be before the rumor spreads to half the carrying capacity?
(1 point) Suppose that news spreads through a city of fixed size of 800000 people at a time rate proportional to the number of people who have not heard the news. (a.) Formulate a differential equation and initial condition for ?(?), the number of people who have heard the news ?t days after it has happened. No one has heard the news at first, so ?(0)=0. The "time rate of increase in the number of people who have heard the...
In a laboratory setting, scientists are testing the claim that a certain contagious disease spreads at a rate that is proportional to the number of interactions between those that are infected x(t) and those that are disease-free y(t). To do this, the scientists begin with a population of 500 mice. Ten of the mice are removed, infected with the contagious disease, and then returned to the rest of the population. 1. Find a mathematical model that estimates the number of...
Question 1. First, we study a model for a disease which spreads quickly through a population. The rate of new infections at time t is proportional to the number of people who are currently infected at time t, and the number of people who are susceptible at time t. (a) Explain why I(t) satisfies the first-order ODE dI BI(N − 1) dt where ß > 0 is a constant. (b) Find the equilibrium solution(s) of the ODE (in terms of...
2. Two differential equations modeling problems follow. Do at least one of them (a) i. If N is the (fixed, constant) population in among residents can often be modeled as follows: Let x = x(t) be the number of people who have heard caught the disease by time t days. Then the disease spreads via the interactions between those who have the disease, and those who don't. The rate of transmission of the disease is thus proportional to the product...
9. The rate of change of y is proportional to y. A given business is losing market, therefore the monthly sales are plunging exponentially. At month 3 the sales were 4 (million) dollars.. At month 5 the sales were 1 (million) dollars. How much were the sales at month 02 hint: it is obvious that at month zero the sales were greater than 4 million dollars, 10. This follows the logistic model. Mr. ZeMarcelino put 10 animals on his farm...
Results for this submission Entered Answer Preview Result -k (y-a) -k(y - a) correct correct -kt a +(1-a) e correct 65 65 incorrect At least one of the answers above is NOT correct (1 point) As you know, when a course ends, students start to forget the material they have learned. One model (called the Ebbinghaus model) assumes that the rate at which a student forgets material is proportional to the difterence between the material currently remembered and some positive...
1. Let X and Y be two random variables.Then Var(X+Y)=Var(X)+Var(Y)+2Couv(X,Y). True False 2. Let c be a constant.Then Var(c)=c^2. True False 3. Knowing that a university has the following units/campuses: A, B , the medical school in another City. You are interested to know on average how many hours per week the university students spend doing homework. You go to A campus and randomly survey students walking to classes for one day. Then,this is a random sample representing the entire...