Question

A laboratory culture contains 150 bacteria. After twenty minutes, the culture contains 300 bacteria. After one hour, the culture contains 1200 bacteria. Make a conjecture about the rate at which the bacteria grow.

Answer 1

This type of situation applies first order type of equation.  In this case, the equation is ln( A0/A1) = kt. A is the number of bacteria cultured. A0 is equal to 150. when A1 is 300, t is 20 minutes. that is ln (150/300) = k *20 the other condition is represented by ln (A0/1200) = 60k. k is equal to -0.0347. hence the first order equation is equal to ln (150/A1) = -0.0347 t