To model the growth of a bacteria culture that starts with 500 bacteria and doubles in size every 3 hours, we use the concept of exponential growth. The general form of an exponential growth function can be described by the formula:
N(t) = N0 * ekt
Where:
- N(t) is the number of bacteria at time t,
- N0 is the initial quantity (in this case, 500),
- k is the growth constant,
- t is time (in hours), and
- e is the base of the natural logarithm (approximately equal to 2.71828).
However, since we know that the bacteria double in size every 3 hours, we can express this doubling behavior in our model. The doubling time indicates that the population multiplies by 2 after each period of 3 hours. This gives us:
N(t) = 500 * 2(t/3)
In this formula:
- 500 is the initial number of bacteria,
- 2 represents the doubling effect every 3 hours, and
- t/3 indicates how many 3-hour intervals have passed in time t.
To summarize, the exponential model that describes the growth of the bacteria culture over time is:
N(t) = 500 * 2(t/3)
This function effectively captures the growth of the bacteria as it doubles every 3 hours. By plugging in different values of t, you can easily calculate the expected population size at any given time!