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Exponential Growth

Exponential Growth. Photos by: Matthew Field, www.wikipedia.com and Tom Brennan, www.reptilezofaz.com. Cholla Cactus. N=1. N=4. N=16. Cholla Cactus. N=64. Number of cactus. Is there a way to calculate this without drawing trees?.

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Exponential Growth

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  1. Exponential Growth Photos by: Matthew Field, www.wikipedia.com and Tom Brennan, www.reptilezofaz.com

  2. Cholla Cactus N=1 N=4 N=16

  3. Cholla Cactus N=64

  4. Number of cactus Is there a way to calculate this without drawing trees? Can you figure out the number of trees on year 8, without calculating all of the other years?

  5. Cholla populations • In year 8, there will be… 65,536 cholla! • Does this seem realistic? Why or why not? • Carrying Capacity- The maximum number of plants or animals that can live in a place.

  6. Lizards Western Banded Gecko (Coleonyxvariegatus) 3 female offspring per year How many geckos will there be in 5 years? 35 = 243

  7. Lizards What if there were 2 geckos at the start? 3 female offspring per year Western Banded Gecko (Coleonyxvariegatus)

  8. Growth Rate Equation N=S*λt Time New population Growth rate Starting population

  9. Growth Rate Equation N=S*λt Time New population Growth rate Starting population N=(2)*35 N=486 geckos

  10. Growth Rate Equation N=S*λt Time New population Growth rate Starting population Two important points: λ does not need to be a whole number. λ>1 means the population is increasing, and λ<1 means the population is decreasing.

  11. Growth Rate Equation N=S*λt Time New population Growth rate Starting population Example: What if there were 500 geckos, and each year there were only 95% as many geckos as before. How many would there be in 8 years? Answer: 500*(0.95)8 = About 332

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