Monday

December 22, 2014

December 22, 2014

Posted by **sean** on Wednesday, May 9, 2007 at 7:10pm.

The number, N, of people who have heard a rumor spread by mass media at time, t, in days is modelled by

N (t) = a / 1+ be^ -kt

a. If 50 people have heard the rumour initially and 300,000 people hear the rumour eventually, find a and b

b. If the rumour is initially spreading at the rate of 500 people per day, find k.

Thanks.

for a)

initially ---> t=0

so 50 = a/(1 + be^0)

50 = a/(1+b)

a=50 + 50b ----- (#1)

I will interpret "eventually" to mean t --> ∞

then e^(-large) ---> 0

and 300000=a/(1+0), so a=300000

putting this back in #1 gives b=5999

so N(t) = 300000/(1 + 5999e^-kt)^-1

for b)

N'(t) = -300000((1 + 5999e^-kt)^-2)(e^-kt)(-k)

"initially" the rate is 500 means

500 = -300000(1+5999)^-2 * (1)(-k)

..

..

I got k=10, check my arithmetic please

**Answer this Question**

**Related Questions**

Math - The number, N, of people who have heard a rumor spread by mass media by ...

Calculus - The number, N, of people who have heard a rumor spread by mass media ...

Calculus I, differentiation - The number, N, of people who have heard a rumor ...

Math - I can't calculate 1 as the answer given to the following problem. I keep ...

calculus - The rate at which a rumor spreads through an Alpine village of 400 ...

calculus - N(t) = 650 1+649 e−0.5 t . (You may wish to sketch a graph of ...

Calculus - N(t) = 650/1+649 e^−0.5 t (b) How many people will have heard ...

Relationships - 1.When you spread a rumor about so and so like so and so. What ...

Math - #5. If a rancher has one cow with a contagious disease in a herd of 1000...

math - number of people who hear a rumor after t hours is N(t) = 2000/ 1 + 499e...