Final answer:
An exponential function for bacterial growth in a lab culture can be represented as N(t) = N0 × 2^(t/T), where N(t) is the number of bacteria at time t, N0 is the initial amount, t is time, and T is the doubling time.
Step-by-step explanation:
An exponential function that represents the growth of bacteria in a lab culture can be represented by the formula N(t) = N0 × 2^(t/T), where:
- N(t) is the number of bacteria at time t,
- N0 is the initial number of bacteria,
- 2 is the base of the exponential function which reflects the doubling nature of the growth,
- t is the time in hours,
- and T is the doubling time in hours (often approximately 1 hour for bacteria in favorable conditions).
For example, if we start with 1000 bacteria (N0=1000) and the doubling time is 1 hour (T=1), after 3 hours (t=3) we would expect to have N(3)=1000 × 2^(3/1) = 8000 bacteria.
The function showcases the characteristic of exponential growth, where the rate of increase itself escalates over time. This leads to a rapid escalation in the total number of bacteria, particularly when resources are plentiful and environmental conditions are ideal.