Join now for JEE/NEET and also prepare for Boards Join now for JEE/NEET and also prepare for Boards. Register Now
Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
What is differential in describe? What is differential in describe?
Suppose two students at your school start a rumor. How could we describe the spread of the rumor throughout the school population? Could we determine a functionSsuch thatS(t)approximates the number of people that know the rumor at a time arbitrary timet,wheretis measured in, say, hours?We'll begin by trying to decide what the graph ofSmight look like. Assume thatMis the population of your school and thatMis sufficiently large that it makes sense to model discrete numbers of students with a continuous function. Thus, ifS(3) = 127.8, we'll predict that the number of students who know the rumor after3hours is approximately128.Study the six graphs below. For each graph, decide whether or not it could be the graph of the functionS. In each case, give the reasons for your decision.Possible Graphs of SDescribe three conditions that the graph ofSshould satisfy.We could try to assemble a list of conditions that the graph ofSshould satisfy, i.e., conditions onSitself, hoping in this way to determine a model functionS. However, it will be easier to shift our attention todS/dt, the rate of change in the number of students who know the rumor -- the rate of spread of the rumor.Describe three conditions thatdS/dt, the rate of spread of the rumor, should satisfy. Keep in mind that we are describing the rate of change of the number of students who know the rumor. Suppose for example, that you know the number of "rumor-aware" students at two o'clock. What factors might determine the number of rumor-aware students at three o'clock? Consider the nature of the rumor itself, conditions at your school, and at least one condition that changes as the rumor spreads.Here are some possible factors you might have listed in Item 3.
Suppose two students at your school start a rumor. How could we describe the spread of the rumor throughout the school population? Could we determine a functionSsuch thatS(t)approximates the number of people that know the rumor at a time arbitrary timet,wheretis measured in, say, hours?
We'll begin by trying to decide what the graph ofSmight look like. Assume thatMis the population of your school and thatMis sufficiently large that it makes sense to model discrete numbers of students with a continuous function. Thus, ifS(3) = 127.8, we'll predict that the number of students who know the rumor after3hours is approximately128.
HereMis the total number of students in the school andkis a constant that depends on both the juiciness of the rumor the average number of contacts between students. Remember that the symbolsSanddS/dtare not constants, but functions oft.
We assume thatkincreases with juiciness and with an increase in the average number of contacts. Thus, ifdS/dtsatisfies this relation, then the rate of spread of the rumor is greater for juicy rumors than it is for "dry" rumors and increases as the average number of contacts increases. So we have satisfied two of the four conditions listed above.
also incorporates our two additional conditions (restated below).
is called a "first-order differential equation" since it involves only the function and itsfirstderivative. On the other hand, the differential equation
is asecond-orderdifferential equation.
does not include all the factors you listed that control the rate of spread of the rumor. If you feel that a factor has been omitted, explain why, and rewrite the differential equation to include this factor.
under what circumstances will the rate of spread of the rumor will be0? ( There is more than one.)
RuchiAskiitians Faculty
Ruchi
Askiitians Faculty
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -