Question

Erosion gradually reduces the size of a small Pacific island that has a current area of just 480 acres. If the island’s area decreases at an annual rate of 0.1%. Find the multiplier for the rate of exponential decay.

Answer 1

\(A = 480 e^{-kt}\), where A = the area after t years.
when t = 1 year (annual)

we have \(A = 0.1(480) = 480 e^{-k}\)

\[0.1=e^{-k}\]
\[k=-\ln(0.1)\]