2025 CHS PRELIM P2 Q1

Jane bought an electric car in January 2025. After purchase, the value of the car, \(\$V\), diminishes over time and can be modelled by \(V = 38000e^{-kt}\), where \(k\) is a positive constant and \(t\) is time measured in years. The value of the car is expected to be \(\$29000\) after 3 years of driving. Jane intends to sell her car when its value drops to half of its original value.

Showing clear mathematical calculations, find the year that Jane is likely to sell her electric car.[5]