Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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The dove population on Honeydoom farms has become slightly invasive, doves have far out-competed the endangered Emerald Sparrows in the area – causing their near. The local animal control board would like to begin culling the dove population in order to ensure the survival of the Emerald Sparrow, but the control board will cease any culling when the population of sparrows and doves are equivalent, they will begin culling in one year. You believe that the current trends in population suggest that an equal dove to sparrow ratio can be expected in a fairly short period. You are asked for proof.
Population growth can be modeled using the equation n(t)= n0e^rt where n0 is the initial population, is the rate of growth, and t is time in decades.
Let us suppose we have a population of sparrows ns(t), with an initial population of ns0 and a population of doves nd(t), initial population of nd0, It has been observed that the doves decrease at a rate of 200 per year and the sparrows increase at a rate of 20 per year.
When the populations were first measured it was estimated that the population followed a ratio of ns0/nd0=1/4
Determine the time in decades when ns(t)/nd(t)=1
How many years is this? The animal control board begins culling in one year; would this make any sense?
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