Final answer:
Exponential growth in bacterial populations is observed. The rate of growth can be calculated using the doubling time and the formula for growth rate. In this case, the rate of growth is approximately 13.24%.
Step-by-step explanation:
Exponential growth is commonly observed in bacterial populations. In this case, the bacterial population starts with 100 bacteria and grows to 600 bacteria in 7 hours. To find the rate of growth, we need to calculate the population doubling time, which is the time it takes for the population to double in size.
To calculate the doubling time, we can use the formula: Doubling Time = Time / (log(base 2) (Final Population / Initial Population)). Plugging in the values, Doubling Time = 7 / (log(base 2) (600 / 100)) ≈ 1.895 hours.
The growth rate, r, can be calculated using the formula: r = (log(base 2) (Final Population / Initial Population)) / Time. Plugging in the values, r = (log(base 2) (600 / 100)) / 7 ≈ 0.1324.
Finally, to convert the growth rate to a percentage, we multiply it by 100. Therefore, the rate of growth is approximately 13.24%.