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Sam purchased a new car for $17,930. The value of the car depreciated by 19% per year. When he trades the car in after x years, the car is worth no more than $1,900.

Fill in the values of a, b, and c to complete the exponential inequality of the form a(b)x ≤ c that can be used to determine the number of years after which the car is worth no more than $1,900.

Respuesta :

sqdancefan

Answer:

  • a=17930
  • b=0.81
  • c=1900
  • 17930·0.81^x ≤ 1900

Step-by-step explanation:

The decay factor for 19% per year depreciation is 1 - 0.19 = 0.81, so the exponential expression for the value of the car after x years is ...

  17930·0.81^x

We want to write an inequality that compares this value to $1900, so that inequality will be ...

  17930·0.81^x ≤ 1900

Comparing this to the given form, we see that ...

  a = 17,930

  b = 0.81

  c = 1,900

_____

The solution is x ≥ 10.6521.

Answer:

17930*0.81^x ≤ 1900

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