In 1980 the population of alligators in a particular region was estimated to be 1700. In 2007 the population had grown to an estimated 5000. Using the Malthusian law for population growth, estimate the alligator population in this region in the year 2020. The alligator population in this region in the year 2020 is estimated to be (Round to the nearest whole number as needed.)
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Step 1: Calculate the growth rate (R) using the formula R = log(5000/1700) / 27 Show more…
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In 1980 the population of alligators in a particular region was estimated to be 1300. In 2006 the population had grown to an estimated 5000. Using the Malthusian law for population growth, estimate the alligator population in this region in the year 2020. The alligator population in this region in the year 2020 is estimated to be 14,108. (Round to the nearest whole number as needed.)
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Researchers have developed a mathematical model that can be used to estimate the number of teeth $N(t)$ at time $t$ (days of incubation) for Alligator mississippiensis, where $$N(t)=71.8 e^{-896 e^{-0.0688}}$$ Source: Journal of Theoretical Biology. a. Find $N(65)$ , the number of teeth of an alligator that hatched after 65 days. b. Find $\lim _{t \rightarrow \infty} N(t)$ and use this value as an estimate of the number of teeth of a newborn alligator. (Hint: See Exercise $65 .$ ) Does this estimate differ significantly from the estimate of part a?
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