Relative growth rate problem

In summary, the bacterium Escherichia coli divides into two cells every 20 minutes in a nutrient-broth medium. The initial population of 90 cells experiences a relative growth rate that is dependent on the size of the population at a given time. To determine the growth rate, we need to know the size of the population at time t and the type of growth the population experiences. The function for the population at time t must be exponential. We can calculate the relative growth rate by comparing the growth rate to the size of the population at a given time.
  • #1
bobbarkernar
48
0
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 90 cells.


the question asks to find the relative growth rate, if we measure t in hours.


im not exactly sure what they are asking for?
if someone can point me in the right direction.
 
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  • #2
What does growth rate mean, and what does "relative growth rate" mean?
 
  • #3
well growth rate is that rate at which a certain population increases or decreases. so relative growth rate is the rate at which a population increases or decreases relative to time?
 
  • #4
No, "relative growth rate" means the growth rate relative to the SIZE OF THE POPULATION at the same time!

1. So, if the population at time t is x(t), what is its growth rate at time t?
2. And what is its relative growth rate?
3. What type of growth do you think the bacterium population experiences?
4. What type of function must x(t) be?
5. Use the info to determine x(t)!
6. Calculate the relative growth rate!
 

1. What is a relative growth rate problem?

A relative growth rate problem is a mathematical problem that involves finding the percentage change in a quantity over a certain time period. It is commonly used in fields such as biology, economics, and finance to analyze growth patterns.

2. How do you calculate the relative growth rate?

The relative growth rate can be calculated by dividing the absolute change in quantity by the original quantity and then multiplying by 100 to get a percentage. The formula is (Final value - Initial value) / Initial value x 100.

3. What is the difference between relative growth rate and absolute growth rate?

Relative growth rate measures the percentage change in a quantity, while absolute growth rate measures the actual change in quantity. For example, if a population increases from 100 to 120, the relative growth rate is 20%, while the absolute growth rate is 20 individuals.

4. What are some real-world applications of relative growth rate problems?

Relative growth rate problems can be applied to analyze population growth, economic growth, and investment returns. They can also be used to track the spread of diseases and the growth of bacteria in a laboratory setting.

5. How can relative growth rate problems be solved?

Relative growth rate problems can be solved by using the formula mentioned in question 2 and plugging in the given values. Additionally, graphing the data and using the slope of the line can also help in solving these problems. Computer software and calculators can also be used to quickly calculate the relative growth rate.

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