[tex]925\text{ km}^2[/tex]
Explanation
Exponential decay function describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula
[tex]\begin{gathered} f\lparen t)=a\left(1-r\right)^t \\ where\text{ a is the initial value} \\ r\text{ is the rate of decay\lparen in decimals}) \\ t\text{ is the time} \end{gathered}[/tex]
Step 1
a)
Let
[tex]\begin{gathered} a=2600 \\ r=8.25\text{ \%}=\frac{8.25}{100}=0.0825 \\ t=12 \end{gathered}[/tex]
b) now, replace in the formula
[tex]\begin{gathered} f\operatorname{\lparen}t)=a\left(1-r\right)^t \\ f\lparen12)=2600\left(1-0.0825\right)^{12} \\ f\lparen12)=2600\left(0.9175\right)^{12} \\ f\lparen12)=2600\left(0.35585483838\right) \\ f\lparen12)=925.222 \\ rounded \\ f\lparen12)=925 \end{gathered}[/tex]
therefore, the answer is
[tex]925\text{ km}^2[/tex]
Blank: 925
I hope this helps you
