Sure, let's solve these problems step by step.
We have the function:
[tex]\[ p(x) = 22,285 \times (0.92)^x \][/tex]
### (a) Cost of a 4-year-old car
To find the cost of a 4-year-old car, we will substitute [tex]\( x = 4 \)[/tex] into the function:
1. Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[ p(4) = 22,285 \times (0.92)^4 \][/tex]
2. Calculate [tex]\( (0.92)^4 \)[/tex]:
[tex]\[ (0.92)^4 \approx 0.71639 \][/tex]
3. Multiply this result by 22,285:
[tex]\[ 22,285 \times 0.71639 \approx 15,965 \][/tex]
So, the cost of a 4-year-old car is approximately [tex]\(\$15,965\)[/tex].
### (b) Cost of a 7-year-old car
To find the cost of a 7-year-old car, we will substitute [tex]\( x = 7 \)[/tex] into the function:
1. Substitute [tex]\( x = 7 \)[/tex] into the function:
[tex]\[ p(7) = 22,285 \times (0.92)^7 \][/tex]
2. Calculate [tex]\( (0.92)^7 \)[/tex]:
[tex]\[ (0.92)^7 \approx 0.56952 \][/tex]
3. Multiply this result by 22,285:
[tex]\[ 22,285 \times 0.56952 \approx 12,432 \][/tex]
So, the cost of a 7-year-old car is approximately [tex]\(\$12,432\)[/tex].
In summary:
- A 4-year-old car should cost approximately [tex]\(\$15,965\)[/tex].
- A 7-year-old car should cost approximately [tex]\(\$12,432\)[/tex].
