(a)If the birth rate and death rate of the number of bacteria are proportional to the number of bacteria present, what is the population as a function of time. (b)What is the limiting situation for increasing time? Interpret it.

If the growth rate of the number of bacteria at any time t is proportional to the number present at t and doubles in 1 week, how many bacteria can be expected after 2 weeks? After 4 weeks?

A tank contains 400 gal of brine in which 100 lb of salt are dissolved. Fresh water runs into the tank at a rate of 2gal/min. The mixture, kept practically uniform by stirring, runs out at the same rate. How much salt will there be in the tank at the end of 1 hour?

In a population, the birth rate and death rate are calculated as follows: Birth Rate = Number of Births ÷ Population Death Rate = Number of Deaths ÷ Population For example, in a population of 100,000 that has 8,000 births and 6,000 deaths per year, the birth rate and death rate are: Birth Rate = 8,000 $\div$ 100,000 = 0.08 Death Rate = 6,000$\div$100,000 = 0.06 Design a Population class that stores a population, number of births, and number of deaths for a period of time. Member functions should return the birth rate and death rate. Implement the class in a program. Input Validation: Do not accept population figures less than 1, or birth or death numbers less than 0.

What should be the 14/6C content (in percent of y_o) of a fossilized tree that is claimed to be 3000 years old?