Question

Identify the exponential function that correctly fits the situation below.

The size of a rainforest is currently decreasing at a rate of 17% per year. If there are currently 230,000 square miles of rainforest, then about how many square miles of rainforest will there be in t years?

A.
F = 230,000(0.17)t
B.
F = 230,000(0.83)t
C.
F = 230,000(1.17)t
D.
F = 230,000(1.83)t

Answer 1

The correct exponential function for the size of a rainforest decreasing at a rate of 17% per year is F = 230,000(0.83)^t, which corresponds to Option B.

Step-by-step explanation:

To identify the exponential function that correctly fits the situation of the decreasing size of a rainforest, we need to consider that the size is decreasing at a rate of 17% per year. Since the decrease is by 17%, the remaining percentage each year is 100% - 17% = 83% or 0.83 in decimal form. Therefore, the size of the rainforest after t years will be 83% of the previous year's size.

The correct exponential function for the situation provided is:
F = 230,000(0.83)t.

This means Option B is the correct answer. We can note that t represents the number of years, and F represents the size of the rainforest in square miles after t years.

Answer 2

The correct answer is B). Indeed, after the first year, we are going to left out with 230,000 * 0.83 square miles of rainforest. It can be modelled with a function according to this example. Then, the answer is:

`230,000*(0.83)^(t)`