Question: A model for the spread of a rumor is given by the equation where p(t) is the proportion of the population that knows the rumor

A model for the spread of a rumor is given by the equation

p(t) 1 + ae-kt

where p(t) is the proportion of the population that knows the rumor at time t and a and k are positive constants.
(a) When will half the population have heard the rumor?
(b) When is the rate of spread of the rumor greatest?
(c) Sketch the graph of p.

p(t) 1 + ae-kt

Step by Step Solution

★★★★★

3.48 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a which is when half the population will hav... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction of the population who have heard the rumor and the fraction who have not heard the rumor....

A model for the spread of contagious diseases is obtained by assuming that the rate of spread is proportional to the number of contacts between infected any non-infected persons, who are assumed to...

what + wathawul Who Murdered Maxwell Murphy? During a cold and rainy March night, the police were summoned to the home of the rich and famous art collector Maxwell Murphy. Someone had murdered Mr....

The Pacific halibut fishery has been modeled by the differential equation dt dy = ky(1 - where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t (measured...

Write a differential equation that is satisfied by y. Solve the differential equation. and part c.) as well One model for the spread of a rumor is that the rate of spread is proportional to the...

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...

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...

Help with my project, please! In this project, you will explore the behavior of exponential functions by using them to model the spread of disease. It is important to note that, while meaningfill in...

When an advantageous gene appears in a population, or when an infectious person appears in a population of susceptibles, a traveling wave can often appear. In the first case, the advantageous gene...

Answer each question appropriately. Suppose the area of the region between the graph of a positive continuous function fand the x-axis from x=a to x = bis 13 square units. Find the area between the...

What is printed by the following python algorithm? # Define a stack class in Python class Stack definit (self): self.items= def Push(self, item): self.items.append(item) def Pop(self) def return...

Please show the steps. 1 . Convert ( 6 4 DF ) 1 6 to octal. 2 . Convert ( 9 3 7 ) 1 0 to Binary - Coded Decimal ( BCD ) ( 1 0 points ) The following is a string of ASCII characters whose bit patterns...

What is trawling?

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If F = P i + Q j and Py = Qx in an open...

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. There is a vector field F such that curl F =...

A vector field F, a curve C, and a point P are shown. (a) Is C F dr positive, negative, or zero? Explain. (b) Is div F(P) positive, negative, or zero? Explain. P R RR

Assume the following information: Sandy has $100,000 to conduct triangular arbitrage. What will be Sandy's profit from implementing this strategy? $1900.74 $1,920.00. $6,629.85. $5,820.00

Complete the Balance sheet and sales information in the table that follows for J. White Industries using the following financial data: Total Assets Turnover: 1.5 Gross Profit margin on sales: (Sales...

Sybil, age 40 is single and supports her dependent parents who live with her and also supports her grandfather who is in a nursing home. She has an AGI of $80,000 and itemized deductions of $8,000