Question

Inspectors for the U.S. Department of Agriculture test a sample of ground beef for the bacterium E. coli. The sample is found to have a bacteria count of 150 colony-forming units per milliliter (CFU/mL). The sample is kept at a temperature of 100° F, and 2 hours later the meat has a count of 13,300 CFU/mL.

(a) Find the instantaneous growth rate r (per hour) for the bacteria count in the sample. (Round your answer to three decimal places.)
r =  

(b) Find an exponential model f(t) = Ce^rt for the bacteria count in the sample, where t is measured in hours. (Round r to three decimal places.)

f(t) =

(c) What does the model predict the bacteria count will be after 3 hours? (Round your answer to the nearest whole number.)


(d) How long will it take for the bacteria count to reach one million CFU/mL? (Round your answer to two decimal places.)


(e) Find the doubling time for the population of E. coli bacteria. (Round your answer to two decimal places.)

Answer 1