type the correct answer in the box. sam purchased a new car for $17,930. the value of the car depreciated by…

type the correct answer in the box. 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. a(b)^x ≤ c

type the correct answer in the box. 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. a(b)^x ≤ c

Answer

Answer:

$a = 17930$, $b=0.81$, $c = 1900$

Explanation:

Step1: Identify the initial - value

The initial value of the car is the purchase price. So $a = 17930$ (the initial amount of money Sam paid for the car).

Step2: Calculate the depreciation factor

The car depreciates by 19% per year. So the value of the car each year is $(1 - 0.19)$ of its value the previous year. Then $b=1 - 0.19=0.81$.

Step3: Identify the maximum - value

The car is worth no more than $1900$. So $c = 1900$.