Suppose the rate of growth of a bacterial population (N cells/liter) is described by: dN/dt = kN -1000. The terms represent growth of the bacterial cells (with growth constant k), and predation (eating) of bacteria by a small population of protozoa which does not change over the time period of interest. Assume t is in seconds.
a. What are the units of k?
b. What are the units of the 1000 term on the right hand side?
c. If the initial value of N is 1 million/L, what values of k would allow the initial rate of change of N to be positive?
d. What Euler's method numerical simulation equation would you use to model this process?