Question

A bacterial culture is known to grow at a rate proportional to the amount present after 1 hour, 1000 strands of the bacteria are observed in the culture, and after 4 hours, 3000 strands. Find the number of strands of bacteria originally in the culture.

Answer 1

This type of situation applies first order type of equation.  In this case, the equation is ln( A0/A1) = kt when A1 is 1000, t is 1 hour. that is ln (A0/1000) = k the other condition is represented by ln (A0/3000) = 4k The two equations tell that Ao is equal to 694 strands.