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

Question

anonymous · Answer

help

mathmale · Answer

The basic formula for exponential decay is

$$y=y _{0}e ^{kt}$$

mathmale · Answer

The initial area of the island is 480 acres; this occurs when t=0.  Thus, $$y=y _{0}e ^{kt}\rightarrow 480=480e ^{k(0)}$$...or simply let $$y _{0}=480~acres$$ up front.

mathmale · Answer

After 1 year, the area is 10% less, or 90% (0.90) of its previous size:$$0.90(480~acres)=(480~acres)e ^{1k}$$...where that '1' represents the elapsed time (1 year).

Please solve this equation for k and you'll have your answer.