After 5.4 years, the value of the car will be half the initial value.
We know that the value decreases by 12% each year.
Then the value of the car can be modeled with an exponential decay, written as:
[tex]V(t) = A*(1 - 12 \% /100 \%)^t = A*(1 - 0.12)^t = A*(0.88)^t[/tex]
Where A is the initial value, and t is the number of years.
The value will be halved when:
[tex](0.88)^t = 0.5[/tex]
We need to solve that, to do it, we can apply the natural logarithm to both sides, so we get:
[tex]Ln(0.88^t) = Ln(0.5)\\\\t*Ln(0.88) = Ln(0.5)\\\\t = Ln(0.5)/Ln(0.88) = 5.4[/tex]
This means that after 5.4 years, the value of the car will be half the initial value.
If you want to learn more about exponential decays:
https://brainly.com/question/11464095
#SPJ2
