Posted by **Brian** on Sunday, February 24, 2013 at 10:14pm.

The number, N, of people who have heard a rumor spread by mass media by time, t, is given by N(t)=a(1−e−kt). There are 6 million people in the population, who hear the rumor eventually. If 5% of them heard it on the first day, find the percentage of the population who have heard the rumor after 5 days.

I found N'(t)=(ae^-(bx))+axe^-(bx)

and i figure a=6M*.05=300000, but i cannot find the %population after 5 days. any help would be awesome, Thanks in advance!

- Calculus I, differentiation -
**Steve**, Monday, February 25, 2013 at 3:18pm
N(t) = a(1 - e^-kt)

After 1 day, t=1, and we have

.05a = (1 - e^-k)

.05 = 1 - e^-k

0.95 = e^-k

k = -ln 0.95 = 0.0513

so,

N(t) = a(1 - e^-0.0513t)

So, by the end of day 5,

N(5) = a(1 - e^-.2565) = .226a = 22.6%

have heard the rumor

## Answer this Question

## Related Questions

- Calculus - The number, N, of people who have heard a rumor spread by mass media ...
- Math - The number, N, of people who have heard a rumor spread by mass media by ...
- 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 ...
- Math - I can't calculate 1 as the answer given to the following problem. I keep ...
- math - Could u help me with this question. The number, N, of people who have ...
- calculus - The rate at which a rumor spreads through an Alpine village of 400 ...
- Calculus - The number of people that hear a rumor follows logistic growth. In a ...
- math - number of people who hear a rumor after t hours is N(t) = 2000/ 1 + 499e...
- calculus - A rumor spreads through a population in such a way that "t" hours ...