1. A population of protozoa develops with a constant relative growth rate of 0.5041 per member per day. On day zero the population consists of four members. Find the population size after eight days. (Round your answer to the nearest whole number.)
2. A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 54 cells.
(a) Find the relative growth rate. (Assume t is measured in hours.)
(b) Find an expression for the number of cells after t hours.
(c) Find the number of cells after 8 hours.
(d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.)
(e) When will the population reach 20,000 cells? (Round your answer to two decimal places.)
3. A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 260.
(a) Find an expression for the number of bacteria after t hours.
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.)
(c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.)
(d) When will the population reach 10,000? (Round your answer to one decimal place.)