The total number of inches R(t) of rain during a storm of length t hours can be approximated by

R(t) = (at)/(t+b),where a and b are positive constants that depend on the geographical locale.

Sketch a graph of R on paper. As t -> infinity,what value does R(t) approach? (Assume a = 4 and b = 8.)
R(t) = 4

This means that as the time of the storm increases, the total amount of rainfall approaches 4 in.

1) Find the equation(s) of the vertical asymptote(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

2) Find the equation of the horizontal asymptote.

3) Find the points of intersection with the horizontal asymptote. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

4)a) The intensity I of the rainfall (in in./hr) is defined by I=R(t)/t. Sketch the graphs of R and I on the same coordinate plane for t > 0. As t → infinity,what value does I(t) approach?

b) This means that as the time of the rainfall increases, the intensity of rainfall approaches...

5) As the time of the storm increases(t → infinity),what happens to R(t) and I(t)?

Multiple choice. Choose one:

a)Both the amount of rainfall and the intensity of rainfall decrease.

b)The amount of rainfall increases, and the intensity of the rainfall decreases.

c) The amount of rainfall decreases, and the intensity of the rainfall increases.

d) Both the amount of rainfall and the intensity of rainfall increase.