A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days.   If the bacteria is untreated, the rate of growth of the population is directly proportional to the size of the population, dPdt=ktdPdt=kt. The general solution to this differential equation is P=CektP=Cekt, where P is the current size of the population and t is the number of days since measurement began.   If untreated, how long until the population of the bacteria colony reaches 100,000? (Use 3 decimal places)

A tree farm starts with ten trees. Tree growth is expected to follow logistic growth with a first-order growth rate constant of r = 0.16 yr ' to a maximum of 8,000 trees. Write the equation that relates the number of trees (N) to time (1). What are the values of No, r, and K? Plot the number of trees over time if no harvesting occurs. Go out to about 70 years. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY? Determine the standing crop. (The standing crop is the number of trees at steady state when harvesting at the MSY.)

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there are100 milligrams of the material present and if after two years it is observed that 5 percent of the original mass has decayed, find (a) an expression for the mass at any time t and (b) the time necessary for 10 percent of the original mass to have decayed.