1 Answer

AlvaroAV · Answer 1 · 2023-04-22T16:28:18+0000

$925\text{ km}^2$

Step-by-step 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

$\begin{gathered} f\lparen t)=a\left(1-r\right)^t \\ where\text{ a is the initial value} \\ r\text{ is the rate of decay\lparen in decimals}) \\ t\text{ is the time} \end{gathered}$

Step 1

a)

Let

$\begin{gathered} a=2600 \\ r=8.25\text{ \%}=(8.25)/(100)=0.0825 \\ t=12 \end{gathered}$

b) now, replace in the formula

$\begin{gathered} f\operatorname{\lparen}t)=a\left(1-r\right)^t \\ f\lparen12)=2600\left(1-0.0825\right)^(12) \\ f\lparen12)=2600\left(0.9175\right)^(12) \\ f\lparen12)=2600\left(0.35585483838\right) \\ f\lparen12)=925.222 \\ rounded \\ f\lparen12)=925 \end{gathered}$

therefore, the answer is

$925\text{ km}^2$

Blank: 925

I hope this helps you

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