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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?

Verified Answer :

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

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

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

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

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