How Many Aphids by August 31 Under Ideal Conditions?

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SUMMARY

The discussion centers on calculating the population growth of aphids under ideal conditions, starting with a single female aphid on June 1 and extending to August 31. Each female aphid reproduces every 48 hours, producing two female offspring before dying. By analyzing the reproductive cycle and using a function to model the growth over 93 days, participants can derive the total aphid population at the end of the period. The key takeaway is the exponential growth pattern similar to cell division, which can be expressed mathematically.

PREREQUISITES
  • Understanding of exponential growth models
  • Basic knowledge of parthenogenesis in aphids
  • Familiarity with functions and time variables in mathematical modeling
  • Ability to create and interpret diagrams for population dynamics
NEXT STEPS
  • Develop a mathematical model for aphid population growth based on the reproductive cycle
  • Learn about exponential growth functions and their applications in biology
  • Explore the concept of parthenogenesis and its implications in population studies
  • Practice drawing population growth diagrams to visualize reproductive patterns over time
USEFUL FOR

Students studying population dynamics, biologists interested in insect reproduction, and anyone involved in ecological modeling or pest management strategies.

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Homework Statement


In summer months, female aphids reproduce by parthenogenesis, giving birth to females from unfertilized eggs. These females mature within 24h and begin reproducing in the same way. Assume that each female aphid produced two females the day after she herself is born, and and then she dies.

If there is a single female aphid on June 1, how many aphids would there be under ideal conditions by August 31?


Homework Equations


Not aware of any.


The Attempt at a Solution



I am not really sure since there are no equations given in the book. Also, all I know is that there are 93 days during this period of time. But I don't know how to find the population.

Could anyone please help? Thanks.
 
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You can think of this problem as exactly analogous to cell division. In cell division, the parent gives rise to two "daughter's", in this case, after 48 hours of incubation. You should be able to find a formula for that.

48 hours = 24 hours from egg-laying to maturity + 24 hours later egg-laying begins
 
Another way to start, is by drawing a diagram of what is happening in your problem, and label your diagram with respect to time (days gone by). You can then develop your own formula by looking at your numbers after drawing several generations. You are developing a function f(t), where t is time.
[Hint:how does time change in your question?].
 

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