Tisha buys a car for $30,319. Her car immediately starts depreciating, losing 10% of its value every year. How much will the car be worth in 2 years?round your answer to the nearest cent

Respuesta :

In this problem

we have an exponential decay function of the form

[tex]y=a(1-r)^x[/tex]

where

y is the value of the car

x is the number of years

a is the initial value

r is the rate

we have

a=$30,319

r=10%=10/100=0.10

substitute given values

[tex]\begin{gathered} y=30,319(1-0.10)^x \\ y=30,319(0.90)^x \end{gathered}[/tex]

For x=2 years

substitute

[tex]y=30,319(0.90)^2[/tex]

y=$24,558.39