Question

A mutation occurs in a single bacterium that causes it to produce a new enzyme. This enzyme helps the bacterium process nutrients more efficiently, increasing the bacterium's odds of survival.
Every 30 minutes, the bacteria in the colony divide, passing their genes on to their offspring. Some bacteria survive, while others do not. Because resources are limited, the colony has a steady population of 114 bacteria.

The bacterial colony is shown below at three different time intervals.

Assume that the survival trend shown in the diagram continues. At 3.0 hours, the mutant bacteria will make up
percent of the entire colony.

Answer 1

Bacteria express exponential growth models, meaning their population growth is dense-independent and proportional to the population size. In the exposed example, assuming a colony of 114 cells at 3.0 hours, the mutant bacteria will make up 56.14 % of the entire colony.

What is exponential growth?

Exponential growth is one model of population growth together with the logistic growth model.

Populations that experience exponential growth models show an increase in proportion to their size. The increase in the population size depends on the individual's reproduction rate: a population that grows at constant exponential rate gains individuals faster as the population increases in size.

This model states that populations live in an environment with unlimited resource availability, so the density factor does not influence population growth. There is no density-dependence effect nor competition for resources. Natality and mortality rate do not depend on density. There is a constant growth rate per capita, and it is proportional to the population size.

Bacteria usually experience exponential growth.

In the exposed example, we can see that

• At 0 hours, there were only one bacteria expressing the new enzyme
• After 1 hour, there were four bacteria expressing the enzyme
• After 2 hours, there were 16 bacteria expressing the enzyme.

We can assume that each bacteria divides every 30 minutes (half an hour). So each bacteria produces 4 new cells every hour.

0 hours ------- 1 bacteria with the enzyme

1 hour --------- 4 bacteria with the enzyme (1 x 4)

2 hours ------- 16 bacteria with the enzyme (4 x 4)

3 hours --------64 bacteria with the enzyme (16 x 4).

Each of the 16 cells present after 2 hours got divided and produced 4 new cells, resulting in 64 cells after 3 hours.

The population growth rate is proportional to the population size.

114 bacteria ------ 100% of the population

64 bacteria -------X = (64 x 100) / 114 = 56.14%

At 3.0 hours, the mutant bacteria will make up 56.14 % of the entire colony.

You can learn more about exponential growth at

brainly.com/question/28596571

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