This exponential growth is shown in the following graph where population size Y-axis is compared with time in days X-axis. Exponential growth produces a characteristic J-shaped curve because the population keeps on doubling until it gradually curves upward into a very steep incline.
If the graph were plotted logarithmically rather than exponentially, it would assume a straight line extending upward from left to right. Sixteen days of exponential growth in Wolffia microscopica. W olffia plants have the fastest population growth rate of any member of the kingdom Plantae. Under optimal conditions, a single plant of the Indian species Wolffia microscopica may reproduce vegetatively by budding every 30 hours.
One minute plant could mathematically give rise to one nonillion plants or 1 x 10 30 one followed by 30 zeros in about four months, with a spherical volume roughly equivalent to the size of the planet earth! Note: This is purely a mathematical projection and in reality could never happen! The following illustration shows a comparison of the size of one minute wolffia plant, roughly intermediate between a water molecule and the planet Earth!
I f a water molecule is represented by 10 0 , then a wolffia plant is about 10 20 power larger than the water molecule. The earth is about 10 20 power larger than a wolffia plant, or 10 40 power larger than the water molecule. National Park Service. Resource management brief — horses. Can you identify the carrying capacity in these populations of the fictitious smiling rainbow fish? Although examining how the size of the population changes over time is informative, it neglects to take into account how much space the population is occupying.
How dense a population is can impact survival and be influenced by a number of factors. You may have heard of density in a chemistry or physics class before. In those cases, density typically refers to how dense an object is as seen in the figure below.
Population density is similar to object density, except it refers to the number of individuals or organisms instead of the number of particles. Factors that influence population size, such as a drought or drop in prey, are categorized into one of two types:. We can recognize the following data: Therefore, we have: Therefore, there will be 12 bacteria after 4 hours. Solution Here, we have the same formula as the previous exercise, but now we have to find the time knowing the final quantity.
We can recognize the following data: Therefore, we have: Therefore, the population of bacteria will become 50 after Solution We already have a given formula:. We have to calculate the population using time. Therefore, we substitute to get: Therefore, the population in the community after 10 years will be 10 Therefore, we have: Thus, we can model the population growth of the community with the formula.
Assuming we start with one bacterium, how many bacteria will we have at the end of 96 minutes? Solution We know that bacteria grow continuously, so we have to use the formula: The bacteria doubles every 5 minutes, so after 5 minutes, we will have 2.
We use this to find the value of k : Now, we form the equation using this value of k and solve using the time of 96 minutes:. Exponential growth — Exercises to solve Practice using the exponential growth formulas with the following exercises. Solve the exercises and select an answer. Check your answer to verify that you selected the correct one. The population of a community was 12 After 20 years it was found that the population grew to 16 What will the population be after 50 years?
Choose an answer The actual population was 2,,, so we were pretty close. We'll be doing more with populations after I've taught you some more stuff. At 5pm, you count 26, alien bacteria in your petrie dish. If the growth rate is 2. We use first party cookies on our website to enhance your browsing experience, and third party cookies to provide advertising that may be of interest to you.
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