High School

Identify the exponential function that correctly fits the situation below.

The size of a rainforest is currently decreasing at a rate of 50% per year. If there are currently 210,000 square miles of rainforest, then about how many square miles of rainforest will there be in \( t \) years?

A. \( F = 210,000(0.5)^t \)
B. \( F = 210,000(1.5)^t \)
C. \( F = 220,000(1.4)^t \)
D. \( F = 210,000(0.5)^t \)

Answer :

The proper exponential function for describing the decrease in rainforest size by 50% per year from a starting point of 210,000 square miles is F = 210,000(0.5).

The correct exponential function that fits the situation of rainforest size decreasing at a rate of 50% per year, starting with 210,000 square miles, is F = 210,000(0.5) .

To determine the amount of rainforest in square miles there will be in t years, we apply this exponential decay model. In our formula, 0.5 represents a 50% reduction each year. Therefore, after t years, the size of the rainforest will be F = 210,000(0.5) square miles.