Question

Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, what is the car’s value after 5 years​

Answer 1

$8874

Explanation:

At the end of the first year, Terrence's car depreciated by 15%. We can calculate the resulting value with the expression ($20,000)(1 - 0.15) = $17000. The end of the second year is another 15% reduction, on the already lower value. For x years, we can write an expression that gives the new value at the end of the year:

f(x) ($20,000)(1 - 0.15)^x

After 5 years the new value would be ($20,000)(1 - 0.15)^5

($20,000)(1 - 0.15)^5 = 8874.11 or $8874