High School

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. \( f = 220,000(1.4)^t \)

B. \( f = 210,000(0.95)^t \)

C. \( f = 210,000(0.5)^t \)

D. \( f = 210,000(1.5)^t \)

Answer :

The answer is option c. f = 210,000 (0.5) t.

The rainforest is decreasing in size, so the rate of change is a fraction less than 1. Since each year the size is multiplied by a factor to get to the next year's size, that factor must be less than 1.

Of the above options, only answer choice (c) has a factor that is less than 1.

Choice (c) f = 210,000 (0.5) t. multiplies by 0.5 each year, which represents a 50% decrease.

Let's look at an example:

Year 1: 210,000 * 0.5 = 105,000 square miles

Year 2: 105,000 * 0.5 = 52,500 square miles

This demonstrates the continual decrease in size.

The answer is option c. f = 210,000(0.5)t

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