For exponential functions, they are defined by the general formula:
[tex]f(x)=ab^x[/tex]
From the graph given in the question, we can deduce that
when
[tex]\begin{gathered} x=0,y=200 \\ x=1,y=180 \end{gathered}[/tex]
With this, we can derive the values of a and b
so that
[tex]\begin{gathered} 200=a\times b^0 \\ 200=a \end{gathered}[/tex]
Similarly, we can get b by substituting the value of a=200 and y=180 when x=1 into the equation
[tex]\begin{gathered} 180=200\times b^1 \\ b=\frac{180}{200}=0.9 \end{gathered}[/tex]
Thus the formula is
[tex]y=200(0.9)^x[/tex]
The 0.9 means that there is a loss of 10% every year
Therefore
The correct answer is
$200 at a 10% loss per year
