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 76 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. (Round your answer to the nearest thousand cells) (d) Find the rate of growth (in billion

The initial population of pigs in a farm is 125. Given that the growth rate per year is 7.5%, determine the number of pigs after 57.5 months (express your answer to the nearest whole number, t must be in years).

The amount of the radioactive element Pragelium present in a sample can be calculated using a modelof the form A = A0ekt. The half-life of Pragelium is 13 years. Determine the value of k, rounding youranswer to four decimal places.

A population of bacteria grows to twice its original amount in 3 hours. How long will it take to grow to 5 times its original amount? (Round your answer to three decimal places.)

A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into a nutrient broth, the culture grows at a rate proportional to its size. After 1.5 hours, the population has increased to 925.   (a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.)   (b) Find the number of bacteria after 6 hours. (Round your answer to the nearest whole number.)   (c) Find the rate of growth (in bacteria per hour) after 6 hours. (Round your answer to the nearest whole number.)