1.  Solve HW 2 using Mathcad.  Which software do you prefer and why?

2.  A 300-gallon hot tub has been idle for some time, and the water is at an ambient temperature of 70 degrees F.  You want to add hot water, at a temperature of 140 degrees F, and at a rate of 3 gallons per minute.  The temperature of the water in the tub as a function of time can be modeled by the equation:

T(t) = T_in - (T_in - T₀)e^(-Q*t/V)

T(t) is the tub temperature (T) as a function of time (t)
T_in in the inflow temperature (given: 140 F)
T₀ is the tub temperature at t=0 (given: 70 F)
Q is the flowrate into the tub (3 gpm, where gpm = gallons per minute)
t is time in minutes
V is the tub volume (300 gallons)

a)  What is the temperature in the tub after one hour?

b)  If the temperature you like is 104 F, when should you get in?

c)  Plot the tub temperature as a function of time.

3.  Horton's Laws are used in hydrology to describe watershed characteristics.  The smallest tributaries are assigned the "order" of one, and as the tributaries join and form larger streams, the order increases.  Here is an example of how streams are ordered:

A plot of the stream order (i) on the x axis, versus the log of the number of streams of each order (N_i) usually results in a straight line.  This type of plot is known as a semi-log plot, since only one axis is a log scale.  A semi-log plot can be created by computing the log of Ni and plotting those values, or by plotting Ni and changing the y-axis scale to logarithmic.  Plot the following data (which do not come from the above figure) using Mathcad, and determine if the semi-log plot is reasonably straight.  Which method of creating the semi-log plot is better and why?