Question

The equation N(t) = 600/1 + 49e^0.7t models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N(t) approach? Interpret your answer.

 

How many people started the rumor?   

 

N(t) approaches  number?

 

N(t)

 is limited by the number of poeple who started the rumor.

N(t)

 is limited by the carrying capacity of the town.

N(t)

 is limited by the rate at which the rumor spreads.

N(t)

 is limited by the number of days it takes for the entire population to hear the rumor.

N(t)

 is not limited by any value and increases without bound.

 

Answer 1

$\displaystyle N(t)=\frac{600}{1+49e^{0.7t}}\\ \quad\\ 1]\ \text{How many people started the rumor?}\\ \text{At time zero, that is when }t=0,\\ N(0)=12\text{ people started the rumor.}\\ \quad\\ 2]\ \text{As t increases without bound, what value does N(t) approach?}\\ \text{Since}\ \lim_{t\rightarrow \infty}N(t)=0\\ \text{Thus, as t increases without bound, we have N(t) approaches 0.}\\ \quad\\ 3]\ \text{Finally, from 2 above we have that N(t) is limited by the number of days it takes for}\\ \text{ the entire population to hear the rumor. Since as t increases N(t) approaches 0.}$