A car is sold for $22,000. After one year, the value of the car is $18,700. 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.

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

y = b (1 - r) ^x

Where

y represents the value of the car after x years.

x represents the number of years.

b represents the initial value of the car.

r represents rate of decay.

From the information given,

A = $18700

P = $22000

x = 1

Therefore,

18700 = 22000 (1 - r) ^1

18700/22000 = (1 - r) ^1

0.85 = 1 - r

r = 1 - 0.85

r = 0.15

Therefore, the exponential function is

y = 22000 (1 - 0.15) ^x

y = 22000 (0.85) ^x

Y = 22000 - 3300x

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