# Relationship between growth rate doubling time

### Content - Population growth and doubling time

SUMMARY: The relations between growth rate, generation time distribution and the number growth rate constant, and 7 is the mean generation time (in. Describe the relationship both generically and also give a specific formula relating the two quantities. Selected Answer: Growth rate is the increasing rate of the number of organisms in a population and doubling time is the amount of time it takes for a quantity to double in size. Populations can grow at a constant rate, thus the Rule of 70 can be used to approximate the doubling time of a population that is growing at a fixed rate of growth.

However, it should be noted that the explanations below refer to a constant rate of growth, which as we note, is not as applicable to countries now as it was in the past. Exponential Growth A quantity grows exponentially when its increase is proportional to what is already there.

Exponential growth has surprising consequences. Significant gains can be made by simply relying on exponential growth over time.

One way of saying this is that the longer you wait on your investment, the faster your returns come in. In the following graph, you can see that over time, returns increase dramatically. There are also clear disadvantages to exponential growth.

When populations continue to grow, the impact of growth becomes increasingly significant over time. Because of the nature of exponential growth, "when things get bad, they get bad in a hurry".

In 10 years, the population will double topeople, in another 10 years it will double again topeople, and ten years after that it will double again topeople.

The following graph shows this exponential population growth. The shape of the curve is identical to the interest rate graph above! The Rule of 70 The Rule of 70 states that to find the doubling time of a quantity growing at a given annual percentage rate, divide the percentage number into 70 to obtain the approximate number of years required to double.

This is called exponential growth. In reality, exponential growth is only part of the bacterial life cycle, and not representative of the normal pattern of growth of bacteria in Nature.

When a fresh medium is inoculated with a given number of cells, and the population growth is monitored over a period of time, plotting the data will yield a typical bacterial growth curve Figure 3 below. The typical bacterial growth curve. When bacteria are grown in a closed system also called a batch culturelike a test tube, the population of cells almost always exhibits these growth dynamics: When their growth becomes limited, the cells stop dividing stationary phaseuntil eventually they show loss of viability death phase.

Note the parameters of the x and y axes. Growth is expressed as change in the number viable cells vs time.

## Exponential growth, doubling time, and the Rule of 70

Generation times are calculated during the exponential phase of growth. Time measurements are in hours for bacteria with short generation times. Four characteristic phases of the growth cycle are recognized. Immediately after inoculation of the cells into fresh medium, the population remains temporarily unchanged.

### What is Doubling Time and How is it Calculated? - Population Education

Although there is no apparent cell division occurring, the cells may be growing in volume or mass, synthesizing enzymes, proteins, RNA, etc. The length of the lag phase is apparently dependent on a wide variety of factors including the size of the inoculum; time necessary to recover from physical damage or shock in the transfer; time required for synthesis of essential coenzymes or division factors; and time required for synthesis of new inducible enzymes that are necessary to metabolize the substrates present in the medium.

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• Doubling time

The exponential phase of growth is a pattern of balanced growth wherein all the cells are dividing regularly by binary fission, and are growing by geometric progression. The cells divide at a constant rate depending upon the composition of the growth medium and the conditions of incubation. The rate of exponential growth of a bacterial culture is expressed as generation time, also the doubling time of the bacterial population. Exponential growth cannot be continued forever in a batch culture e.