\ \

A group of friends created a video parody of several popular songs and posted it online. \ \

A model that can be used to estimate the number of people that viewed the video is \ \

, Where is the days since the video was originally posted. \ \

(a) \ \

The logistic function . \ \

Graph: \ \

Graph the logistic function on . \ \

\ \

\ \

(b) \ \

Find the function values at and  for graph by using tracing or table feature of the

graphing utility in part (a). \ \

Therefore, , and . \ \

Find . \ \

Graph the function up to . \ \

Plot the point on the graph at . \ \

\ \

Observe the graph: \ \

The function value at is . \ \

Therefore number of people who watched the video after two months() is . \ \

\ \

(c) Find . \ \

Observe the graph in part(b): \ \

As tends to large positive values , then increases without bound. \ \

Thus, we may conclude that infinite amount of people may view the video. \ \

. \ \

\ \

(a) \ \

\ \

(b) , , and . \ \

Number of people who watched the video after two months() is . \ \

(c) .