## Mathematics

1- A bacteria culture doubles every 30 minutes. a. If the initial concentration is 20 cells/ml, construct an exponential function y = Cat to describe the growth of the bacteria, where t represent hours.        Create a table of values that shows the number of cells/ml from t =0 tot =8 hours.  t (in hours) 0 1 2 3 4 5 6 7 8 y (cells/ml)    b. Approximately how long will it take the bacteria concentration to reach 5000 cells/ml?
1. The body eliminates drugs by metabolism and excretion.  To predict how frequently a patient should receive a drug dosage, the physician must determine how long the drug will remain in the body.  This is usually done by measuring the half-life of the drug.  The accompanying graph shows a drug’s concentrationC t( ), in milligrams in the body over time, t , in hours. a. What is the initial concentration of the drug?  b. Estimate the half-life of the drug    c. Construct an equation that approximates the curve.  Specify the units of your variables.  d. How long would it take five half-lives to occur?  Approximately how many milligrams of the original dose would be left then?  e. Show algebraically how you would find the hourly decay factor.