Final answer:
The exponential growth of a bacterium with a growth rate of 25% per day starting from 0.5 gram over 2 weeks can be calculated using an exponential function. After 14 days, the initial amount multiplies exponentially, resulting in a J-shaped growth curve.
Step-by-step explanation:
Understanding Exponential Growth in Bacteria
Given that a certain bacterium grows at an exponential growth rate of 25% per day, starting with 0.5 gram, we can use the formula for exponential growth to calculate the amount of bacteria after 2 weeks. There are 7 days in a week, so 2 weeks amount to 14 days. The formula for exponential growth is:
N = N0 * e^(rt)
Where:
- N is the final amount of substance
- N0 is the initial amount of substance (0.5 gram)
- e is the base of the natural logarithm (approximately 2.71828)
- r is the growth rate (0.25, or 25% per day)
- t is the time in days (14 days)
Plugging the values into the formula we get:
N = 0.5 * e^(0.25*14)
Calculating this gives us N = 0.5 * e^(3.5). After evaluating the exponential function, we round to the nearest tenth of a gram to find the final amount of bacteria.
Thus, using unlimited resources, we would see an accelerating population growth rate and a significant increase in the bacteria's population after 2 weeks. When plotted, this would result in a J-shaped growth curve.