Question

A small island in the middle of a river is eroding away. Each year, the island has 85% of the area from the previous year. After one year the island has an area of 10.2 thousand square yards. Graph the sequence and describe the pattern. How much of the island is left after 6 years?

Answer 1

see the attachment for a graph

4.53 thousand square yards remain after 6 years

Explanation:

The area can be described by an exponential equation that multiplies the area by 0.85 when the time variable increases by 1 year. Such an equation might be ...

a(t) = 10.2·0.85^(t-1)

The graph of this is attached.

After 6 years, the equation predicts

a(6) = 10.2·0.85^(6-1) ≈ 4.53 thousand square yards

of island will remain.