Final answer:
The question concerns a principle of exponential growth applied to a bacteria colony. This can be represented by the differential equation dn/dt = kn, which shows that the bacterial growth rate is proportional to the current number of bacteria. Solving this equation gives us a formula for the number of bacteria at any time, given the initial number and the growth rate.
Step-by-step explanation:
The question involves a principle of exponential growth, which is often found in various scientific fields such as biology and population studies. In this specific context, the bacteria in the colony are growing at a rate that is proportional to the current number of bacteria, n. This can be represented mathematically by the differential equation dn/dt = kn, where dn/dt represents the rate of change in the number of bacteria, n is the current number, and k is a constant representing the proportional rate of growth.
In simple terms, this means that the more bacteria there are, the faster they grow, which is characteristic of exponential growth. To solve this equation, we use the method of separation of variables, leading to the solution n(t) = n(0)*e^(kt), where e is the base of natural logarithm, t is the time, and n(0) is the initial number of bacteria. This formula allows us to predict the number of bacteria at any time t, given the initial number and the growth rate.
Learn more about Exponential Growth