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Exemplo 6 de Algebra and Trigonometry, 6.7 Exponential and Logarithmic Models
Problema e solução em inglês, como no livro original.
An influenza epidemic spreads through a population rapidly, at a rate that depends on two factors: The more people who have the flu, the more rapidly it spreads, and also the more uninfected people there are, the more rapidly it spreads. These two factors make the logistic model a good one to study the spread of communicable diseases. And, clearly, there is a maximum value for the number of people infected: the entire population.
For example, at time there is one person in a community of 1,000 people who has the flu. So, in that community, at most 1,000 people can have the flu. Researchers find that for this particular strain of the flu, the logistic growth constant is Estimate the number of people in this community who will have had this flu after ten days. Predict how many people in this community will have had this flu after a long period of time has passed.
Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.
We substitute the given data into the logistic growth model
Because at most 1,000 people, the entire population of the community, can get the flu, we know the limiting value is To find we use the formula that the number of cases at time is from which it follows that This model predicts that, after ten days, the number of people who have had the flu is Because the actual number must be a whole number (a person has either had the flu or not) we round to 294. In the long term, the number of people who will contract the flu is the limiting value,
O Try It do livro logo depois deste exemplo: mesma ideia, outros números. Só a resposta é dada.
Using the model in Example 6, estimate the number of cases of flu on day 15.
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