Answer: [tex]56,900\left( 0.919\right)^x[/tex]
Step-by-step explanation:
Given
Marcos purchased a sailboat for [tex]\$56,900[/tex]
Each year the boat will decrease in value by [tex]8.1\%[/tex]
After 1 year it is
[tex]\Rightarrow 56,900-56,900\times 0.081\\\Rightarrow 56,900\left( 1-0.081\right)\\[/tex]
after another year it becomes
[tex]\Rightarrow 56,900\left( 1-0.081\right)-56,900\left( 1-0.081\right)\times 0.081\\\Rightarrow 56,900\left( 1-0.081\right)\cdot \left( 1-0.081\right)\\\Rightarrow 56,900\left( 1-0.081\right)^2[/tex]
After [tex]x[/tex] years it is
[tex]\Rightarrow 56,900\left( 1-0.081\right)^x[/tex]
[tex]\Rightarrow 56,900\left( 0.919\right)^x[/tex]
