Certainly! Let's go through the problem step by step.
1. Initial Cost of the Car:
Tony bought a car for $20,000. This is the initial value of the car.
2. Annual Decrease Rate:
The value of the car decreases by 12% each year.
3. Understanding the Rate of Decrease:
A 12% decrease can be expressed as multiplying the current value of the car by (1 - 0.12).
Mathematically:
[tex]\[
1 - 0.12 = 0.88
\][/tex]
Therefore, each year the car retains 88% of its value from the previous year.
4. Formulating the Decrease:
To find the value of the car after [tex]\( x \)[/tex] years, we need to multiply the initial value by 0.88 raised to the power of [tex]\( x \)[/tex].
5. General Formula:
The value [tex]\( A(x) \)[/tex] of the car after [tex]\( x \)[/tex] years can be described by the exponential decay formula:
[tex]\[
A(x) = 20000 \times (0.88)^x
\][/tex]
So, the equation that gives the value of the car [tex]\( x \)[/tex] years since Tony bought it is:
[tex]\[
A(x) = 20000 \times (0.88)^x
\][/tex]
This is your desired final expression.
