Answer :
To model a decrease of a quantity by 50% per year, we start with an initial area of the rainforest, which is given as
[tex]$$
A_0 = 210\,000.
$$[/tex]
Since the area is decreasing by 50% each year, this means that every year the area is multiplied by 0.5. Thus, after 1 year the area becomes
[tex]$$
210\,000 \times 0.5 = 105\,000.
$$[/tex]
Following this pattern, after [tex]$t$[/tex] years the area can be described by the exponential function
[tex]$$
F(t) = 210\,000 \cdot (0.5)^t.
$$[/tex]
After comparing with the given multiple-choice options, we see that the correct function is
[tex]$$
\boxed{F = 210\,000(0.5)^t.}
$$[/tex]
[tex]$$
A_0 = 210\,000.
$$[/tex]
Since the area is decreasing by 50% each year, this means that every year the area is multiplied by 0.5. Thus, after 1 year the area becomes
[tex]$$
210\,000 \times 0.5 = 105\,000.
$$[/tex]
Following this pattern, after [tex]$t$[/tex] years the area can be described by the exponential function
[tex]$$
F(t) = 210\,000 \cdot (0.5)^t.
$$[/tex]
After comparing with the given multiple-choice options, we see that the correct function is
[tex]$$
\boxed{F = 210\,000(0.5)^t.}
$$[/tex]