Learning Resources

Investigation 4: Getting a Little Culture

Test yourself (solution)

The following exponential function describes the growth of bacteria in a certain culture: , where E(t) is the number of bacteria and t is the time in hours.

1. The initial number of bacteria occurs at time zero. Substitute t = 0 into the equation:
   
   E(t) = 250 x 3⁰ = 250 x 1 = 250
   
   There are 250 bacteria present initially.
   
   
2. To find the number present after 30 min, substitute t = 0.5 (time has to be in hours) into the equation:
   
   E(t) = 250 x 3^0.5 = 250 x 1.732 = 433
   
   There are approximately 433 present after 30 min.
   
   
3. To find the number present after 1 h, substitute t = 1 into the equation:
   
   E(t) = 250 x 3¹ = 250 x 3 = 750
   
   There are 750 present after 1 hour.
   
   
4. To find the number present after 3 h, substitute t = 3 into the equation:
   
   E(t) = 250 x 3³ = 250 x 27 = 6 750
   
   There are 6 750 present after 3 h.