A car is sold for $22,000. After one year, the value of the car is $16,500. Write an exponential function y to determine the value of the car after x years if the rate of decrease is the same each year.Estimate the value of the car after 4 years. Round the answer to the nearest dollar.

Ledexadvanips

Ledexadvanips

Answered question

2022-08-02

A car is sold for $22,000. After one year, the value of the car is $16,500. Write an exponential function y to determine the value of the car after x years if the rate of decrease is the same each year.Estimate the value of the car after 4 years. Round the answer to the nearest dollar.

Answer & Explanation

Jaiden Gould

Jaiden Gould

Beginner2022-08-03Added 11 answers

car's initial value = $22000
after one year car's value = $ 16,500
let , rate of decrease = r
general form of exponential equation is
y = a ( 1 r ) x
where, y is the final value , a is the initial value and r is rate of derease
so we can write
16000 = 22000 ( 1 r ) 1
solving for r
16 22 = ( 1 r ) r = .2727
now equation becomes
y = 22000 ( 1 .2727 ) x
plugging x = 4 to find value of car after 4 years
y = 22000 ( 1 .2727 ) 4 = 6156
so value of car after 4 years = $ 6156

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