Bacteria are growing in a culture, and their number is increasing at the rate of 7% per hour. Initially, 500 bacteria are present.Determine an equation that gives the number, 𝑁, of bacteria present after 𝑡 hours.
Question
Bacteria are growing in a culture, and their number is increasing at the rate of 7% per hour. Initially, 500 bacteria are present.Determine an equation that gives the number, 𝑁, of bacteria present after 𝑡 hours.
Solution
The situation described is a classic example of exponential growth, which can be modeled by the equation:
N = P * e^(rt)
where:
- N is the final amount of bacteria
- P is the initial amount of bacteria
- r is the growth rate (expressed as a decimal)
- t is the time (in hours)
- e is the base of the natural logarithm (approximately equal to 2.71828)
Given that the initial amount of bacteria (P) is 500 and the growth rate (r) is 7% per hour (or 0.07 when expressed as a decimal), we can substitute these values into the equation to get:
N = 500 * e^(0.07t)
This equation will give the number of bacteria present after t hours.
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