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Answer :
To solve the problem of finding the cost of a car after 7 years, given that its value decreases by 13% each year, follow these steps:
1. Initial Value of the Car: The car initially costs [tex]$46,000.
2. Depreciation Rate: The value of the car decreases by 13% annually. This means that each year, the car retains 87% of its value from the previous year. We calculate this by subtracting the depreciation rate from 1:
\[
1 - 0.13 = 0.87
\]
3. Expression for Depreciation: Over multiple years, the value of the car is multiplied by 0.87 once for each year. Therefore, after 7 years, the expression representing the car's value is:
\[
46000 \times (0.87)^7
\]
4. Calculate the Cost After 7 Years: Plug the values into the expression to get the cost of the car after 7 years:
\[
46000 \times (0.87)^7 = 17,353.72056438018
\]
Thus, after 7 years, the value of the car is approximately $[/tex]17,353.72.
1. Initial Value of the Car: The car initially costs [tex]$46,000.
2. Depreciation Rate: The value of the car decreases by 13% annually. This means that each year, the car retains 87% of its value from the previous year. We calculate this by subtracting the depreciation rate from 1:
\[
1 - 0.13 = 0.87
\]
3. Expression for Depreciation: Over multiple years, the value of the car is multiplied by 0.87 once for each year. Therefore, after 7 years, the expression representing the car's value is:
\[
46000 \times (0.87)^7
\]
4. Calculate the Cost After 7 Years: Plug the values into the expression to get the cost of the car after 7 years:
\[
46000 \times (0.87)^7 = 17,353.72056438018
\]
Thus, after 7 years, the value of the car is approximately $[/tex]17,353.72.
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