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The ocean erodes 3% of an island's beaches each year. The island currently has 2500 acres of beachfront. Write an equation to model the erosion of the beaches?

A) f(x) = 2500(1.03)^x.
B) f(x) = 2500(0.97)^x.
C) f(x) = 2500 - 0.97x.
D) f(x) = 2500(0.03)^x.

User Pakman
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Final answer:

The equation that models the erosion of an island's beaches, given that 3% is eroded each year from a starting point of 2500 acres, is B) f(x) = 2500(0.97)^x.

Step-by-step explanation:

To model the erosion of an island's beaches where the ocean erodes 3% of the beach each year, one must use an exponential decay formula. Since the island currently has 2500 acres of beachfront, and each year 3% is lost, the remaining beachfront can be calculated by reducing the previous year's acreage by 3%. Therefore, the correct formula for each subsequent year, represented by x, would be the initial acreage multiplied by 0.97 (which represents a 3% decrease) to the power of x. The equation that correctly models this situation is B) f(x) = 2500(0.97)^x.

User Vallerie
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