To formulate the exponential inequality for determining the number of years after which Sam's car is worth no more than [tex]$1,900$[/tex], we need to identify the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
Given the details:
- Sam purchased the car for [tex]$17,930, so \( a = 17,930 \).
- The car depreciates by 19% each year, meaning it retains 81% of its value each year. Therefore, \( b = 0.81 \).
- The car is worth no more than $[/tex]1,900 after [tex]\( x \)[/tex] years, so [tex]\( c = 1,900 \)[/tex].
Putting these values into the inequality, we have:
[tex]\[ 17,930(0.81)^x \leq 1,900 \][/tex]
Thus, the values are:
[tex]\[ a = 17,930 \][/tex]
[tex]\[ b = 0.81 \][/tex]
[tex]\[ c = 1,900 \][/tex]
So, the complete inequality will be:
[tex]\[ 17,930(0.81)^x \leq 1,900 \][/tex]
