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Tony bought a new car at a cost of [tex]$\$[/tex] 20,000[tex]$. The value of the car decreases by approximately $[/tex]12 \%[tex]$ each year.
Formulate the equation that gives the value, $[/tex]A(x)[tex]$, of the car $[/tex]x$ years since Tony bought the car.

[tex]\[ A(x) = 20000 \times (1 - 0.12)^x \][/tex]

Sagot :

GinnyAnsweridn
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.
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