A car is sold for 22000 After one year the value of the car

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.
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Solution

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