Mathematics
elysehoughton01
35

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?

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(1) Answers
delfox

[latex]n(t)\approx 190000 toads[/latex]Consider the exponential decay model. In general where [latex]n(t)[/latex] is the number of toads after time [latex]t[/latex] years, [latex] \alpha [/latex] is the initial number of toads, and [latex]r[/latex] is the growth rate of the toads, [latex] \alpha = 430000 [/latex] [latex]r=1-0.055=0.945[/latex]  [100%-5.5%] [latex]n(t)=\alpha r^t[/latex] [latex]n(t)=430000\times0.945^t[/latex] [latex]\therefore n(14)=430000\times 0.945^{14} [/latex] [latex]n(t)=194766.2824...\approx 194766 toads[/latex] Since your question is written to 2 significant figures, [latex]n(t)\approx 190000toads[/latex]

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