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Let's analyze the given formula. $\begin{gathered} H=18\,500e^{\text{-} 0.186t} \end{gathered}$ The number $v(t)$ is the value of the car after $t$ years. We are asked to find the worth of the car after $18$ months, i.e., after ${\color{#0000FF}{1.5}}$ years. Therefore, we will substitute ${\color{#0000FF}{1.5}}$ for ${\color{#0000FF}{t}}$ into the given equation.
$H=18\,500e^{\text{-} 0.186t}$
$H=18\,500e^{\text{-} 0.186({\color{#0000FF}{1.5}})}$
$H\approx 13\,996$