The spread of a rumor in a town can be modeled as N = 500/T, where...
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 + 195eā0.625t 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?
In a town whose population is 2600, a disease creates an epidemic. The number of people N infected t days after the disease has begun is given by the function N(t)- 2600 1+34 -0.6t. Complete parts a) through c) below a) How many are initially infected with the disease (t = 0)? (Round to the nearest whole number as needed.) b) Find the number infected after 2 days, 5 days, 8 days, 12 days, and 16 days. The number infected...
Let P(t) represent the number of people who, at time t, are infected with a certain disease. Let N denote the total number of people in the population. Assume that the spread of the disease can be modeled by the initial value problem: dP/dt = k(N ā P)P, P(0) = P0. At time t = 0, when 100,000 member of a population of 500,000 are known to be infected, medical authorities intervene with medical treatment. As a consequence of this...
The population of toads on an pond can be modeled by the equation where t Pt=120e^-.698t is the number of years since 2000. What was the population in the year 2000? Describe what is happening to the population. Is it growing or shrinking? c.When will there be only 20 toads on the pond?
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...
The spread of CORONA virus is given by the equation,?=?.ertIf there were initially 500 people infected by the virus by March 2020 and t is given in weeks, and r is the growth rate of the virus.I. How many people are infected after 84 days when the growth rate is 0.195? [4 Marks]II. At what rate will cause the infected number of people to rise to 1500 in 21 days? [5 Marks]III. How long will it take for the initial...
The spread of CORONA virus is given by the equation,Q=Q.ertIf there were initially 500 people infected by the virus by March 2020 and t is given in weeks, and r is the growth rate of the virus.I. How many people are infected after 84 days when the growth rate is 0.195? [4 Marks]II. At what rate will cause the infected number of people to rise to 1500 in 21 days? [5 Marks]III. How long will it take for the initial...
The number of bacteria grown in a lab can be modeled by P(t)-300 2t, where t is the number of hours. Which expression equivalent to P(t)? (1) 300 8 (2) 300 16 (3) 300 24 4) 300.22 During physical education class, Andrew recorded the exercise times in minutes and heart rates in beats per minute (bpm) of four of his classmates. Which table best represents a linear model time and heart rate of exercise Student 1 Exercise Heart (in minutes)...
The growth of a certain strain of bacteria can be modeled by (t) = Noekt, where No is the initial number of bacteria, t is the time elapsed in minutes. The doubling time for the growth of the bacteria is 88 minutes. Suppose that there are 4000 bacteria initially present. After how many minutes will there be 67,000 bacteria? 349 minutes 346 minutes 355 minutes 369 minutes 358 minutes Tries 0/3 Submit Answer This discussion is closed. Send Feedback