Ecologists studied the spacing between individual trees in a forest in British Columbia. The probability, or likelihood, that there is at least one tree located in a circle with a radius of x feet can be estimated by P(x) = 1 - e^-1144x. For example, P(7) ≈ 0.55 means that if a person picks a point at random in the forest, there is a 55% chance that at least one tree will be located within 7 feet. See the figure.

(a) Evaluate P(2) and P(20), and interpret the results.

(b) Graph P. Explain why it is logical for P to be an increasing function. Does the graph have a horizontal asymptote? 

(c) Solve P(x) = 0.5 and interpret the result.