A population of 430,000 toads is expected to shrink at a rate of 5.5% per year.
Which is the best prediction for the toad population in 14 years?

Respuesta :

[tex]n(t)\approx 190000 toads[/tex]Consider the exponential decay model.
In general where [tex]n(t)[/tex] is the number of toads after time [tex]t[/tex] years, [tex] \alpha [/tex] is the initial number of toads, and [tex]r[/tex] is the growth rate of the toads,

[tex] \alpha = 430000 [/tex]
[tex]r=1-0.055=0.945[/tex]  [100%-5.5%]
[tex]n(t)=\alpha r^t[/tex]
[tex]n(t)=430000\times0.945^t[/tex]

[tex]\therefore n(14)=430000\times 0.945^{14} [/tex]
[tex]n(t)=194766.2824...\approx 194766 toads[/tex]

Since your question is written to 2 significant figures,
[tex]n(t)\approx 190000toads[/tex]

Answer:

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Explanation:

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I hope this helps

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