Question

Suppose a bacterial culture initially has 300 cells. After 1 hour, the population has increased to 600. (Assuming exponential growth) What is the bacteria population after 4 hours? After how many hours will the bacteria population reach 9600 cells? What is the growth constant ?

Answer 1

The bacterial population after 4 hours is 4800 cells. It will take slightly more than 5 hours for the population to reach 9600 cells. The growth constant or rate is 1 per hour.

Step-by-step explanation:

Given the initial population of the bacterial culture is 300 cells and doubled to 600 cells after 1 hour, each hour the population keeps doubling. This is an example of exponential growth. Hence, the bacteria population after 4 hours would be 300*(2^4) = 4800 cells. To find out after how many hours the bacteria population will reach 9600 cells, we can set up the equation 300*(2^x) = 9600, where x indicates the hours. Solving this, we find x=5.33. So, it will take slightly more than 5 hours for the population to reach 9600 cells. The growth constant, or rate, sometimes denoted by 'k' in the exponential growth formula, is the value that represents how fast a quantity is growing. In this case, as the population doubles each hour, the growth rate 'k' is 1 per hour, often written as 1 hr^-1.

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