Given the problem, the situation can be formulated into an exponential inequality as [tex]\( a(b)^x \leq c \)[/tex]. Here's how to assign the values to [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
- Initial value of the car, [tex]\( a \)[/tex]: Sam purchased the car for \[tex]$17,930, so \( a = 17,930 \).
- Depreciation factor, \( b \): The car depreciates by 19% each year, leaving it with 81% of its value from the previous year. This means \( b = 0.81 \).
- Value after \( x \) years, \( c \): The car's worth should not exceed \$[/tex]1,900 after [tex]\( x \)[/tex] years, so [tex]\( c = 1,900 \)[/tex].
Filling in these values, the inequality becomes:
[tex]\[ 17,930 \cdot (0.81)^x \leq 1,900 \][/tex]
Thus, in the form [tex]\( a(b)^x \leq c \)[/tex]:
- [tex]\( a = 17,930 \)[/tex]
- [tex]\( b = 0.81 \)[/tex]
- [tex]\( c = 1,900 \)[/tex]
So the completed exponential inequality is:
[tex]\[ 17,930 \cdot (0.81)^x \leq 1,900 \][/tex]
