Answer:
[tex]A(t)=(0.902)^t \cdot 1500[/tex] [tex][km^2][/tex]
Step-by-step explanation:
In this problem, the initial area of the forest at time t = 0 is
[tex]A_0 = 1500 km^2[/tex]
After every year, the area of the forest decreases by 9.8%: this means that the area of the forest every year is (100%-9.8%=90.2%) of the area of the previous year.
So for instance, after 1 year, the area is
[tex]A_1 = A_0 \cdot \frac{90.2}{100}=0.902 A_0[/tex]
After 2 years,
[tex]A_2=0.902 A_1 = 0.902(0.902A_0)=(0.902)^2 A_0[/tex]
And so on. So, after t years, the area of the forest will be
[tex]A(t)=(0.902)^t A_0[/tex]
And by substituting the value of A0, we can find an explicit expression:
[tex]A(t)=(0.902)^t \cdot 1500[/tex] [tex][km^2][/tex]
