An underground pipeline is leaking a toxic chemical.

The distance the chemical spreads each year can be defined as .

(a) Graph:

Graph the logistic function for .

(b)

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

graphing utility in part (a).

Therefore, , and .

(c)

Find .

Observe the graph in part(a):

As tends to large positive values, then decreases and close to without bound.

.

(d)

Sum of infinite series is .

Here first term that is distance spread for the first year is and common ratio .

Thus there is no chance of reach the chemical spread to the hospital which meters away from the leak.

(a)

(b) , and .

(c) .

(d) No.